Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 443760.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.w1 | 443760w1 | \([0, -1, 0, -76425, 10143477]\) | \(-30505984/9675\) | \(-15656751999763200\) | \([]\) | \(3784704\) | \(1.8205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 443760.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 443760.w do not have complex multiplication.Modular form 443760.2.a.w
sage: E.q_eigenform(10)