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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 47652.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47652.k1 | 47652i1 | \([0, 1, 0, -173761, 38917712]\) | \(-5914624/3267\) | \(-320483095427773872\) | \([]\) | \(1157328\) | \(2.0625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47652.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 47652.k do not have complex multiplication.Modular form 47652.2.a.k
sage: E.q_eigenform(10)