Show commands:
SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 40425cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40425.br1 | 40425cd1 | \([0, 1, 1, 667217, -109222781]\) | \(17869652393984/13156171875\) | \(-24184538514404296875\) | \([]\) | \(903168\) | \(2.4076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40425cd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40425cd do not have complex multiplication.Modular form 40425.2.a.cd
sage: E.q_eigenform(10)