Properties

Label 8624.j
Number of curves 3
Conductor 8624
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8624.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8624.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8624.j1 8624r3 [0, -1, 0, -6131141, -5841282131] [] 72000  
8624.j2 8624r2 [0, -1, 0, -8101, -505651] [] 14400  
8624.j3 8624r1 [0, -1, 0, -261, 3949] [] 2880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8624.j have rank \(1\).

Modular form 8624.2.a.j

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

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.