Show commands:
SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 241200.ek
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
241200.ek1 | 241200ek1 | \([0, 0, 0, -1575, 64125]\) | \(-2370816/8375\) | \(-1526343750000\) | \([]\) | \(290304\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 241200.ek1 has rank \(1\).
Complex multiplication
The elliptic curves in class 241200.ek do not have complex multiplication.Modular form 241200.2.a.ek
sage: E.q_eigenform(10)