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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 227850.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.a1 | 227850ig1 | \([1, 1, 0, -1010135025, -12394750264875]\) | \(-62008858471273416662401/216436381560000000\) | \(-397867560221131875000000000\) | \([]\) | \(243855360\) | \(3.9668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 227850.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 227850.a do not have complex multiplication.Modular form 227850.2.a.a
sage: E.q_eigenform(10)