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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 49686u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.j1 | 49686u1 | \([1, 1, 0, -384081233, -3135674078571]\) | \(-5022437771811277/497757560832\) | \(-621006686647022613654872064\) | \([]\) | \(25698816\) | \(3.8817\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49686u do not have complex multiplication.Modular form 49686.2.a.u
sage: E.q_eigenform(10)