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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 190575b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.a1 | 190575b1 | \([0, 0, 1, -335775, -64794744]\) | \(5186867200/754677\) | \(609150732775633125\) | \([]\) | \(3870720\) | \(2.1377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 190575b do not have complex multiplication.Modular form 190575.2.a.b
sage: E.q_eigenform(10)