Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 6762.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.u1 6762p1 \([1, 0, 1, -12, -38]\) \(-3451273/9936\) \(-486864\) \([]\) \(1152\) \(-0.22165\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6762.u1 has rank \(1\).

Complex multiplication

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

Modular form 6762.2.a.u

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