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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 30345.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.r1 | 30345bc1 | \([0, 1, 1, -1375597035, 19640181457964]\) | \(-11926249134908509075308544/2246680441062421875\) | \(-54229404167094641314921875\) | \([]\) | \(12096000\) | \(3.9395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 30345.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 30345.r do not have complex multiplication.Modular form 30345.2.a.r
sage: E.q_eigenform(10)