Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 75712.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.x1 | 75712cs1 | \([0, -1, 0, -5633, 401569]\) | \(-31250/91\) | \(-57572015341568\) | \([]\) | \(129024\) | \(1.3273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712.x do not have complex multiplication.Modular form 75712.2.a.x
sage: E.q_eigenform(10)