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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5070c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5070.b1 | 5070c1 | \([1, 1, 0, -2747943, 1769945013]\) | \(-2813198004118489/33177600000\) | \(-27063987569049600000\) | \([]\) | \(212160\) | \(2.5413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5070c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5070c do not have complex multiplication.Modular form 5070.2.a.c
sage: E.q_eigenform(10)