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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6762.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6762.k1 | 6762u1 | \([1, 0, 1, -3995, 112550]\) | \(-174676879/35328\) | \(-1425612228096\) | \([]\) | \(20160\) | \(1.0546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6762.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6762.k do not have complex multiplication.Modular form 6762.2.a.k
sage: E.q_eigenform(10)