Properties

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

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

Elliptic curves in class 12600.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12600.ci1 12600cc3 \([0, 0, 0, -67275, -6716250]\) \(1443468546/7\) \(163296000000\) \([2]\) \(32768\) \(1.3520\)  
12600.ci2 12600cc4 \([0, 0, 0, -13275, 465750]\) \(11090466/2401\) \(56010528000000\) \([2]\) \(32768\) \(1.3520\)  
12600.ci3 12600cc2 \([0, 0, 0, -4275, -101250]\) \(740772/49\) \(571536000000\) \([2, 2]\) \(16384\) \(1.0054\)  
12600.ci4 12600cc1 \([0, 0, 0, 225, -6750]\) \(432/7\) \(-20412000000\) \([2]\) \(8192\) \(0.65884\) \(\Gamma_0(N)\)-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)
 
\(q + q^{7} + 4 q^{11} - 2 q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.