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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5070.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.c1 | 5070b1 | \([1, 1, 0, -133, 1357]\) | \(-1557701041/4199040\) | \(-709637760\) | \([]\) | \(2688\) | \(0.38578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5070.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5070.c do not have complex multiplication.Modular form 5070.2.a.c
sage: E.q_eigenform(10)