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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 300069c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
300069.c1 | 300069c1 | \([0, 0, 1, -6051, -205664]\) | \(-33610706587648/5614591059\) | \(-4093036882011\) | \([]\) | \(795648\) | \(1.1470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 300069c1 has rank \(2\).
Complex multiplication
The elliptic curves in class 300069c do not have complex multiplication.Modular form 300069.2.a.c
sage: E.q_eigenform(10)