Properties

Label 12600cb
Number of curves $6$
Conductor $12600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("12600.ck1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12600cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12600.ck4 12600cb1 [0, 0, 0, -39450, -3015875] [2] 24576 \(\Gamma_0(N)\)-optimal
12600.ck3 12600cb2 [0, 0, 0, -40575, -2834750] [2, 2] 49152  
12600.ck2 12600cb3 [0, 0, 0, -153075, 20002750] [2, 2] 98304  
12600.ck5 12600cb4 [0, 0, 0, 53925, -14080250] [2] 98304  
12600.ck1 12600cb5 [0, 0, 0, -2358075, 1393717750] [2] 196608  
12600.ck6 12600cb6 [0, 0, 0, 251925, 107887750] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 12600cb have rank \(0\).

Modular form 12600.2.a.ck

sage: E.q_eigenform(10)
 
\( q + q^{7} + 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.