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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 82110.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82110.q1 | 82110p1 | \([1, 1, 0, -4172048132, -135120107513136]\) | \(-8031037295101123163637345999575881/3239421604398803614051054080000\) | \(-3239421604398803614051054080000\) | \([]\) | \(183625728\) | \(4.5630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82110.q1 has rank \(0\).
Complex multiplication
The elliptic curves in class 82110.q do not have complex multiplication.Modular form 82110.2.a.q
sage: E.q_eigenform(10)