Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2450r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2450.c1 | 2450r1 | \([1, -1, 0, 18758, -18059084]\) | \(1323/256\) | \(-141237624500000000\) | \([]\) | \(40320\) | \(1.9700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2450r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2450r do not have complex multiplication.Modular form 2450.2.a.r
sage: E.q_eigenform(10)