Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1728.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.i1 | 1728p1 | \([0, 0, 0, -108, -7344]\) | \(-6\) | \(-23219011584\) | \([]\) | \(1152\) | \(0.66837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1728.i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1728.i do not have complex multiplication.Modular form 1728.2.a.i
sage: E.q_eigenform(10)