Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("12100.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12100.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12100.i1 12100g4 [0, -1, 0, -21478508, 38320869512] [2] 622080  
12100.i2 12100g3 [0, -1, 0, -1347133, 594672762] [2] 311040  
12100.i3 12100g2 [0, -1, 0, -303508, 36469512] [2] 207360  
12100.i4 12100g1 [0, -1, 0, -137133, -19099738] [2] 103680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 12100.2.a.i

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

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.