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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 67270r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67270.p1 | 67270r1 | \([1, 0, 1, -84108, -8807112]\) | \(74140932601/5210170\) | \(4624045053635770\) | \([]\) | \(537600\) | \(1.7533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67270r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 67270r do not have complex multiplication.Modular form 67270.2.a.r
sage: E.q_eigenform(10)