Properties

Label 34496.cr
Number of curves $3$
Conductor $34496$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 34496.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34496.cr1 34496de3 \([0, 1, 0, -1532785, -730926659]\) \(-52893159101157376/11\) \(-82824896\) \([]\) \(144000\) \(1.8162\)  
34496.cr2 34496de2 \([0, 1, 0, -2025, -64219]\) \(-122023936/161051\) \(-1212639302336\) \([]\) \(28800\) \(1.0115\)  
34496.cr3 34496de1 \([0, 1, 0, -65, 461]\) \(-4096/11\) \(-82824896\) \([]\) \(5760\) \(0.20680\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34496.cr have rank \(0\).

Complex multiplication

The elliptic curves in class 34496.cr do not have complex multiplication.

Modular form 34496.2.a.cr

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.