Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7728.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7728.f1 | 7728d1 | \([0, -1, 0, 7, -459]\) | \(128000/352107\) | \(-90139392\) | \([]\) | \(2240\) | \(0.20535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7728.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 7728.f do not have complex multiplication.Modular form 7728.2.a.f
sage: E.q_eigenform(10)