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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 100011.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100011.c1 | 100011a1 | \([1, 1, 1, 35551, 4633994]\) | \(4969107733387776623/12093154029532179\) | \(-12093154029532179\) | \([]\) | \(766224\) | \(1.7698\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100011.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100011.c do not have complex multiplication.Modular form 100011.2.a.c
sage: E.q_eigenform(10)