Properties

Label 6762.k
Number of curves $1$
Conductor $6762$
CM no
Rank $0$

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Show commands: 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)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{8} + q^{9} + 3 q^{10} + 2 q^{11} + q^{12} + 7 q^{13} - 3 q^{15} + q^{16} - 4 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display