Show commands:
SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 54720ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54720.cl1 | 54720ef1 | \([0, 0, 0, -27468, 1870992]\) | \(-11993263569/972800\) | \(-185904975052800\) | \([]\) | \(236544\) | \(1.4842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54720ef1 has rank \(0\).
Complex multiplication
The elliptic curves in class 54720ef do not have complex multiplication.Modular form 54720.2.a.ef
sage: E.q_eigenform(10)