Properties

Label 178752.ix
Number of curves $1$
Conductor $178752$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ix1")
 
E.isogeny_class()
 

Elliptic curves in class 178752.ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
178752.ix1 178752cd1 \([0, 1, 0, 204819935, -904335968929]\) \(628805222251722551/597713542447104\) \(-903269483076021803104075776\) \([]\) \(75866112\) \(3.8595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 178752.ix1 has rank \(1\).

Complex multiplication

The elliptic curves in class 178752.ix do not have complex multiplication.

Modular form 178752.2.a.ix

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