Show commands:
SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 19600ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.dw1 | 19600ec1 | \([0, 0, 0, -49000, 4287500]\) | \(-221184/7\) | \(-411771500000000\) | \([]\) | \(138240\) | \(1.5805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600ec1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19600ec do not have complex multiplication.Modular form 19600.2.a.ec
sage: E.q_eigenform(10)