Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 12675q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12675.r1 | 12675q1 | \([0, -1, 1, -14083, 8332443]\) | \(-32768/3159\) | \(-29781034435546875\) | \([]\) | \(67200\) | \(1.8406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12675q1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12675q do not have complex multiplication.Modular form 12675.2.a.q
sage: E.q_eigenform(10)