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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 67830.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67830.e1 | 67830e1 | \([1, 1, 0, -3686063, -2727661083]\) | \(-5538755026536843301110649/5221724874240000000\) | \(-5221724874240000000\) | \([]\) | \(3326400\) | \(2.5139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67830.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 67830.e do not have complex multiplication.Modular form 67830.2.a.e
sage: E.q_eigenform(10)