Properties

Label 117208e
Number of curves $1$
Conductor $117208$
CM no
Rank $1$

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

Elliptic curves in class 117208e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117208.f1 117208e1 \([0, -1, 0, -53769, -7207283]\) \(-570820369408/418447211\) \(-12602853357296384\) \([]\) \(675840\) \(1.7889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 117208e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 117208e do not have complex multiplication.

Modular form 117208.2.a.e

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