Properties

Label 12100.j
Number of curves 4
Conductor 12100
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("12100.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12100.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12100.j1 12100f3 [0, -1, 0, -125033, 17055062] [2] 51840  
12100.j2 12100f4 [0, -1, 0, -109908, 21320312] [2] 103680  
12100.j3 12100f1 [0, -1, 0, -4033, -66438] [2] 17280 \(\Gamma_0(N)\)-optimal
12100.j4 12100f2 [0, -1, 0, 11092, -459688] [2] 34560  

Rank

sage: E.rank()
 

The elliptic curves in class 12100.j have rank \(1\).

Modular form 12100.2.a.j

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + 2q^{7} + q^{9} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.