Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 37440cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.cy1 | 37440cm1 | \([0, 0, 0, -12432, 533536]\) | \(-17790954496/195\) | \(-2329067520\) | \([]\) | \(61440\) | \(0.95163\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 37440cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 37440cm do not have complex multiplication.Modular form 37440.2.a.cm
sage: E.q_eigenform(10)