Show commands:
SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 190575.er
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.er1 | 190575fd1 | \([0, 0, 1, -825, 6531]\) | \(1216512/343\) | \(17509078125\) | \([]\) | \(161280\) | \(0.67242\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575.er1 has rank \(0\).
Complex multiplication
The elliptic curves in class 190575.er do not have complex multiplication.Modular form 190575.2.a.er
sage: E.q_eigenform(10)