Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 392784.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.cm1 | 392784cm1 | \([0, 1, 0, -2558600, 1576666356]\) | \(-3843995587427449/6390046584\) | \(-3079301490937921536\) | \([]\) | \(9144576\) | \(2.4435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 392784.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 392784.cm do not have complex multiplication.Modular form 392784.2.a.cm
sage: E.q_eigenform(10)