Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6048.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6048.k1 | 6048s1 | \([0, 0, 0, -75, 254]\) | \(-375000/7\) | \(-870912\) | \([]\) | \(672\) | \(-0.065155\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6048.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6048.k do not have complex multiplication.Modular form 6048.2.a.k
sage: E.q_eigenform(10)