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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 69366.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69366.e1 | 69366a1 | \([1, 1, 0, -6187, -193283]\) | \(-26198337627891001/550062391296\) | \(-550062391296\) | \([]\) | \(119136\) | \(1.0435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69366.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69366.e do not have complex multiplication.Modular form 69366.2.a.e
sage: E.q_eigenform(10)