Properties

Label 162624.eu
Number of curves $1$
Conductor $162624$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 162624.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.eu1 162624em1 \([0, 1, 0, 917503, -806428449]\) \(50250332/194481\) \(-330585622041531580416\) \([]\) \(5406720\) \(2.6200\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624.eu1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162624.eu do not have complex multiplication.

Modular form 162624.2.a.eu

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} - q^{7} + q^{9} - q^{13} - 3 q^{15} + 5 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display