Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 300042.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
300042.c1 | 300042c1 | \([1, -1, 0, -19764, 804816]\) | \(1171205436932929/298640203776\) | \(217708708552704\) | \([]\) | \(1188096\) | \(1.4607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 300042.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 300042.c do not have complex multiplication.Modular form 300042.2.a.c
sage: E.q_eigenform(10)