Properties

Label 10766e
Number of curves $1$
Conductor $10766$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 10766e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10766.f1 10766e1 \([1, 1, 1, -147, 625]\) \(-351447414193/172256\) \(-172256\) \([]\) \(2320\) \(-0.041537\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10766e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10766e do not have complex multiplication.

Modular form 10766.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} - 4 q^{13} - q^{14} + 3 q^{15} + q^{16} + 4 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display