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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2200.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2200.k1 | 2200g1 | \([0, 0, 0, -100, 500]\) | \(-27648/11\) | \(-44000000\) | \([]\) | \(864\) | \(0.17551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2200.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 2200.k do not have complex multiplication.Modular form 2200.2.a.k
sage: E.q_eigenform(10)