Properties

Label 10766d
Number of curves $1$
Conductor $10766$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 10766d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10766.a1 10766d1 \([1, -1, 0, -19, -11]\) \(781229961/344512\) \(344512\) \([]\) \(4512\) \(-0.24173\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10766d1 has rank \(2\).

Complex multiplication

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

Modular form 10766.2.a.d

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