Properties

Label 11774.m
Number of curves 6
Conductor 11774
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11774.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11774.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11774.m1 11774k6 [1, 1, 1, -2296368, -1340356975] [2] 145152  
11774.m2 11774k5 [1, 1, 1, -143408, -21023087] [2] 72576  
11774.m3 11774k4 [1, 1, 1, -29873, -1641401] [2] 48384  
11774.m4 11774k2 [1, 1, 1, -8848, 316447] [2] 16128  
11774.m5 11774k1 [1, 1, 1, -438, 6959] [2] 8064 \(\Gamma_0(N)\)-optimal
11774.m6 11774k3 [1, 1, 1, 3767, -147785] [2] 24192  

Rank

sage: E.rank()
 

The elliptic curves in class 11774.m have rank \(1\).

Modular form 11774.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{7} + q^{8} + q^{9} + 2q^{12} - 4q^{13} + q^{14} + q^{16} - 6q^{17} + q^{18} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.