Properties

Label 117740.a
Number of curves $1$
Conductor $117740$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 117740.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117740.a1 117740c1 \([0, 0, 0, 26912, 5170468]\) \(14155776/84035\) \(-12796410311740160\) \([]\) \(1375920\) \(1.7726\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 117740.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 117740.a do not have complex multiplication.

Modular form 117740.2.a.a

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