Show commands:
SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 205350ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.a1 | 205350ds1 | \([1, 1, 0, 4308215, -8553499835]\) | \(137868581419655/572735619072\) | \(-36737072580699861811200\) | \([]\) | \(17729280\) | \(3.0124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350ds1 has rank \(1\).
Complex multiplication
The elliptic curves in class 205350ds do not have complex multiplication.Modular form 205350.2.a.ds
sage: E.q_eigenform(10)