strongBSDgenus2/HasegawaWangCurves.magma at main · TimoKellerMath/strongBSDgenus2 · GitHub

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SetLogFile("HasegawaWangCurves.log");

SetDebugOnError(true);

load "verifyBSD.magma";
load "LMFDB-curves.magma";

// The Hasegawa curves from the six-authors paper
// P := PolynomialRing(Rationals()); // defined in "LMFDB-curves.magma"

Hasegawa_curves_with_labels := [
<23, P![-2, 2, -3, 0, 0, -2], P![1, 1, 0, 1], "23.2.a.a">, // not isomorphic to LMFDB curve
<29, P![-2, 2, 2, 0, -3, -1], P![1, 0, 0, 1], "29.2.a.a">, // not isomorphic to LMFDB curve
<31, P![-3, 2, 3, -5, -5, -1], P![1, 0, 1, 1], "31.2.a.a">,
<35, P![-19, -16, -7, -8, 0, -1], P![0, 1, 0, 1], "35.2.a.b">, // not isomorphic to LMFDB curve
<39, P![2, -12, 16, -2, -5], P![1, 0, 0, 1], "39.2.a.b">, // not isomorphic to LMFDB curve
<67, P![0, -1, 0, 0, 0, 1], P![1, 1, 0, 1], "67.2.a.b">,
<73, P![0, 1, 0, -2, 0, -1], P![1, 0, 1, 1], "73.2.a.b">,
<85, P![1, -2, 3, 1, 1], P![0, 1, 1, 1], "85.2.a.b">, // not isomorphic to LMFDB curve
<87, P![-1, 1, -3, 1, -1], P![1, 1, 0, 1], "87.2.a.a">,
<93, P![0, 0, 0, 1, 1, -2], P![1, 0, 1, 1], "93.2.a.a">,
<103, P![0, 0, 0, 0, 1, 1], P![1, 0, 1, 1], "103.2.a.a">,
<107, P![-1, -1, -1, 0, 1], P![1, 0, 1, 1], "107.2.a.a">,
<115, P![0, 1, 1, 2], P![1, 1, 0,1], "115.2.a.b">,
<125, P![-1, -1, 1, 2, 2, 1], P![1, 1, 0, 1], "125.2.a.a">,
<133, P![0, -2, 2, -2, 1, -1], P![1, 0, 1, 1], "133.2.a.a">,
<147, P![1, 0, 1, 1, 2, 1], P![0, 1, 1, 1], "147.2.a.d">,
<161, P![1, 4, 4, 1], P![1, 1, 0, 1], "161.2.a.b">, // not isogenous to LMFDB curve
<165, P![0, -3, 1, 3, 2, 1], P![0, 1, 1, 1], "165.2.a.a">, // not isomorphic to LMFDB curve
<167, P![-1, 0, -1, -1, 0, -1], P![1, 1, 0, 1], "167.2.a.a">,
<177, P![0, 0, 0, 1, 1, 1], P![1, 0, 1, 1], "177.2.a.b">,
<191, P![0, 1, 1, -1], P![1, 1, 0, 1], "191.2.a.a">,
// not in six-authors paper
<205, P![0, -2, 1, 2], P![-1, -1, 0, -1], "205.2.a.e">,
<209, P![1, 1, 2, -2, 2, -1], P![0, 0, 0, -1], "209.2.a.b">,
<213, P![-1, 1, -2], P![-1, -1, 0, -1], "213.2.a.c">,
<221, P![0, -1, 0, 1, 0, 1], P![-1, -1, 0, -1], "221.2.a.c">,
<287, P![-2, 3, -4, 1, 0, -1], P![-1, -1, 0, -1], "287.2.a.b">,
<299, P![-1, -3, -2, 1, 1, -1], P![-1, -1, 0, -1], "299.2.a.d">,
<357, P![3, -3, 5, -2, 2], P![0, 0, 0, -1], "357.2.a.f">
];

// The Wang only curves
Wang_curves_with_labels := [
<65, P![-10, 0, 18, 7, 9, 0, -4], P![1, 0, 0, 1], "65.2.a.b">, // not isogenous to LMFDB curve
<65, P![-1, 6, 40, 20, -32, 10, -1], P![], "65.2.a.c">, // not isomorphic to LMFDB curve
<117, P![-7, -9, -12, -5, -3, 0, -1], P![1, 0, 0, 1], "117.2.a.c">, // not isogenous to LMFDB curve
<125, P![-4, -3, 6, 12, 12, 5, 1], P![1, 1, 0, 1], "125.2.a.b">, // not isogenous to LMFDB curve
<133, P![7, 18, 2, -19, -2, 7, -2], P![1, 1, 0, 1], "133.2.a.c">,
<135, P![-3, -8, 2, -3, 1], P![1, 1, 0, 1], "135.2.a.d">, // not isomorphic to LMFDB curve
<175, P![-1, -2, -4, -2, -1, -1], P![1, 0, 1, 1], "175.2.a.e">, // not isogenous to LMFDB curve
<188, P![1, -2, 1, 1, -1, 1], P![], "188.2.a.a">
];

//SetVerbose("HeegnerPoint", 4);

for i -> NC in Hasegawa_curves_with_labels cat Wang_curves_with_labels do
    N := NC[1];
    C := SimplifiedModel(HyperellipticCurve(NC[2], NC[3]));
    if exists{e : e in LMFDB_curves | e[1] eq N and IsIsomorphic(C, HyperellipticCurve(e[2], e[3]))} then
        printf "Curve #%o associated to newform %o is in the LMFDB\n", i, NC[4];
    elif i eq 4 then
        printf "Omitting curve #%o for newform %o (isogenous to curve in LMFDB)\n", i, NC[4];
    else
      try
          printf "%o:\n", NC[4];
          flag := verifyBSD(C, N);
      catch e
          printf "error for #%o: %o\n", i, e;
      end try;
    end if;
    printf "\n";
end for;