Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 5550.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.k1 | 5550e1 | \([1, 1, 0, -7025, 295125]\) | \(-2454365649169/1035763200\) | \(-16183800000000\) | \([]\) | \(24192\) | \(1.2424\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5550.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5550.k do not have complex multiplication.Modular form 5550.2.a.k
sage: E.q_eigenform(10)