Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.x1 6762w1 \([1, 1, 1, -197, -3823]\) \(-352263793/2313846\) \(-5555544246\) \([]\) \(6048\) \(0.55327\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6762.x1 has rank \(0\).

Complex multiplication

The elliptic curves in class 6762.x do not have complex multiplication.

Modular form 6762.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3q^{5} - q^{6} + q^{8} + q^{9} - 3q^{10} + q^{11} - q^{12} - 6q^{13} + 3q^{15} + q^{16} - 2q^{17} + q^{18} - 2q^{19} + O(q^{20})\)  Toggle raw display