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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 450840.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.r1 | 450840r1 | \([0, -1, 0, -27840, -52893540]\) | \(-1156/585\) | \(-1207660986124968960\) | \([]\) | \(6266880\) | \(2.1487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450840.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 450840.r do not have complex multiplication.Modular form 450840.2.a.r
sage: E.q_eigenform(10)