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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 53130b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.b1 | 53130b1 | \([1, 1, 0, 25581252, 58642887888]\) | \(1851352314787299899532057911/2556487378990533244354560\) | \(-2556487378990533244354560\) | \([]\) | \(13844160\) | \(3.3691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53130b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 53130b do not have complex multiplication.Modular form 53130.2.a.b
sage: E.q_eigenform(10)