Show commands:
SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 135240.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.cp1 | 135240x1 | \([0, 1, 0, -401, -5181]\) | \(-569906176/547515\) | \(-6868028160\) | \([]\) | \(77184\) | \(0.58368\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 135240.cp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 135240.cp do not have complex multiplication.Modular form 135240.2.a.cp
sage: E.q_eigenform(10)