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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 254320r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254320.r1 | 254320r1 | \([0, -1, 0, -445445, 135613357]\) | \(-1183744/275\) | \(-2270815529465753600\) | \([]\) | \(2741760\) | \(2.2417\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 254320r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 254320r do not have complex multiplication.Modular form 254320.2.a.r
sage: E.q_eigenform(10)