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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 39270r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.p1 | 39270r1 | \([1, 1, 0, -77, 231]\) | \(-51520374361/117810\) | \(-117810\) | \([]\) | \(8640\) | \(-0.14546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39270r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 39270r do not have complex multiplication.Modular form 39270.2.a.r
sage: E.q_eigenform(10)