Properties

Label 29624.j
Number of curves $1$
Conductor $29624$
CM no
Rank $2$

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

Elliptic curves in class 29624.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29624.j1 29624c1 \([0, 1, 0, -84, 305]\) \(-340736/49\) \(-9538928\) \([]\) \(4608\) \(0.069922\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29624.j1 has rank \(2\).

Complex multiplication

The elliptic curves in class 29624.j do not have complex multiplication.

Modular form 29624.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} - 2 q^{9} + q^{13} - 2 q^{15} - 8 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display