Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 55470i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55470.f1 | 55470i1 | \([1, 0, 1, -186659, 1896143582]\) | \(-388982677010590321/839808000000000000\) | \(-1552804992000000000000\) | \([]\) | \(2451456\) | \(2.7452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55470i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55470i do not have complex multiplication.Modular form 55470.2.a.i
sage: E.q_eigenform(10)