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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 8050k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8050.f1 | 8050k1 | \([1, -1, 0, 23008, 316416]\) | \(137927116575/84410368\) | \(-824320000000000\) | \([]\) | \(36480\) | \(1.5513\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8050k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8050k do not have complex multiplication.Modular form 8050.2.a.k
sage: E.q_eigenform(10)