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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5070.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.r1 | 5070s1 | \([1, 1, 1, -16260, 799365]\) | \(-2813198004118489/33177600000\) | \(-5607014400000\) | \([]\) | \(16320\) | \(1.2588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5070.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5070.r do not have complex multiplication.Modular form 5070.2.a.r
sage: E.q_eigenform(10)