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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 304.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304.b1 | 304c1 | \([0, -1, 0, -8, 16]\) | \(-31250/19\) | \(-38912\) | \([]\) | \(16\) | \(-0.41718\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 304.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 304.b do not have complex multiplication.Modular form 304.2.a.b
sage: E.q_eigenform(10)