Properties

Label 117975j
Number of curves $1$
Conductor $117975$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 117975j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117975.ce1 117975j1 \([0, -1, 1, -200658, 54417593]\) \(-32278933504/27421875\) \(-759055067138671875\) \([]\) \(2399040\) \(2.1285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 117975j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 117975j do not have complex multiplication.

Modular form 117975.2.a.j

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