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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3822.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3822.k1 | 3822j1 | \([1, 0, 1, -99692, 13864106]\) | \(-19007021070457/3421836288\) | \(-19726205254898688\) | \([]\) | \(33600\) | \(1.8519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3822.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 3822.k do not have complex multiplication.Modular form 3822.2.a.k
sage: E.q_eigenform(10)