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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 8034.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8034.k1 | 8034h1 | \([1, 0, 0, -751641, -250756767]\) | \(46962924452705609230609/27478038929349528\) | \(27478038929349528\) | \([]\) | \(213696\) | \(2.0994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8034.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8034.k do not have complex multiplication.Modular form 8034.2.a.k
sage: E.q_eigenform(10)