Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 75712u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.bg1 | 75712u1 | \([0, 0, 0, -4394, -742586]\) | \(-13824/343\) | \(-232789970236096\) | \([]\) | \(179712\) | \(1.4374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712u do not have complex multiplication.Modular form 75712.2.a.u
sage: E.q_eigenform(10)