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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 34862.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34862.a1 | 34862a1 | \([1, -1, 1, -57, 345]\) | \(-20145851361/35698688\) | \(-35698688\) | \([]\) | \(57728\) | \(0.13954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 34862.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 34862.a do not have complex multiplication.Modular form 34862.2.a.a
sage: E.q_eigenform(10)