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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3675.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3675.k1 | 3675g1 | \([1, 1, 0, -200, 3375]\) | \(-46585/243\) | \(-4651171875\) | \([]\) | \(1800\) | \(0.53927\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3675.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3675.k do not have complex multiplication.Modular form 3675.2.a.k
sage: E.q_eigenform(10)