Properties

Label 12600.ci
Number of curves $4$
Conductor $12600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12600.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12600.ci1 12600cc3 [0, 0, 0, -67275, -6716250] [2] 32768  
12600.ci2 12600cc4 [0, 0, 0, -13275, 465750] [2] 32768  
12600.ci3 12600cc2 [0, 0, 0, -4275, -101250] [2, 2] 16384  
12600.ci4 12600cc1 [0, 0, 0, 225, -6750] [2] 8192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 12600.ci do not have complex multiplication.

Modular form 12600.2.a.ci

sage: E.q_eigenform(10)
 
\( q + q^{7} + 4q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.