Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 13013r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13013.g1 | 13013r1 | \([0, 0, 1, 338, 549]\) | \(884736/539\) | \(-2601650051\) | \([]\) | \(8640\) | \(0.49582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 13013r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 13013r do not have complex multiplication.Modular form 13013.2.a.r
sage: E.q_eigenform(10)