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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 400710q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400710.q1 | 400710q1 | \([1, 0, 1, -12839334, 18606146296]\) | \(-38178173208529/2301696000\) | \(-14111850681315530496000\) | \([]\) | \(32503680\) | \(3.0052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400710q1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400710q do not have complex multiplication.Modular form 400710.2.a.q
sage: E.q_eigenform(10)