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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 400752.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400752.k1 | 400752k1 | \([0, 0, 0, -400756719, -3087943969979]\) | \(-344478821986234930432/72909237159\) | \(-1506559110961168961136\) | \([]\) | \(77414400\) | \(3.4493\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400752.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400752.k do not have complex multiplication.Modular form 400752.2.a.k
sage: E.q_eigenform(10)