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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 121242j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121242.i1 | 121242j1 | \([1, 0, 1, 713776, -252518290]\) | \(187615592384231/237141728784\) | \(-50833435620543730704\) | \([]\) | \(3598848\) | \(2.4673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121242j do not have complex multiplication.Modular form 121242.2.a.j
sage: E.q_eigenform(10)