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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 249090.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.r1 | 249090r1 | \([1, 1, 0, -130855287, -603620175339]\) | \(-14590451544283839961/822700800000000\) | \(-13972390900681132800000000\) | \([]\) | \(76608000\) | \(3.5821\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 249090.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 249090.r do not have complex multiplication.Modular form 249090.2.a.r
sage: E.q_eigenform(10)