Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 405.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405.f1 | 405e1 | \([0, 0, 1, -27, 47]\) | \(36864/5\) | \(295245\) | \([]\) | \(72\) | \(-0.22319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 405.f do not have complex multiplication.Modular form 405.2.a.f
sage: E.q_eigenform(10)