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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 493680.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.r1 | 493680r1 | \([0, -1, 0, 254544, 151654131]\) | \(64347918907136/388153407375\) | \(-11002199016362598000\) | \([]\) | \(7996800\) | \(2.3356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 493680.r do not have complex multiplication.Modular form 493680.2.a.r
sage: E.q_eigenform(10)