Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1380.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1380.e1 | 1380e1 | \([0, 1, 0, -845, 12975]\) | \(-260956266496/145546875\) | \(-37260000000\) | \([]\) | \(1344\) | \(0.73178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1380.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1380.e do not have complex multiplication.Modular form 1380.2.a.e
sage: E.q_eigenform(10)