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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 45177b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45177.h1 | 45177b1 | \([0, 1, 1, 1249441, -716779816]\) | \(44859392/72171\) | \(-347040342741768580179\) | \([]\) | \(1193472\) | \(2.6265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45177b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45177b do not have complex multiplication.Modular form 45177.2.a.b
sage: E.q_eigenform(10)