Properties

Label 10608ba
Number of curves $6$
Conductor $10608$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10608.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10608ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10608.p4 10608ba1 [0, 1, 0, -8624, -311148] [2] 8192 \(\Gamma_0(N)\)-optimal
10608.p3 10608ba2 [0, 1, 0, -8704, -305164] [2, 2] 16384  
10608.p2 10608ba3 [0, 1, 0, -22224, 857556] [2, 4] 32768  
10608.p5 10608ba4 [0, 1, 0, 3536, -1083628] [2] 32768  
10608.p1 10608ba5 [0, 1, 0, -322784, 70467252] [4] 65536  
10608.p6 10608ba6 [0, 1, 0, 62016, 5878260] [4] 65536  

Rank

sage: E.rank()
 

The elliptic curves in class 10608ba have rank \(1\).

Modular form 10608.2.a.p

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} - 4q^{11} + q^{13} - 2q^{15} + q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.