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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1840.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1840.e1 | 1840g1 | \([0, 0, 0, -8, 12]\) | \(-221184/115\) | \(-29440\) | \([]\) | \(144\) | \(-0.43807\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1840.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1840.e do not have complex multiplication.Modular form 1840.2.a.e
sage: E.q_eigenform(10)