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Properties

Label 1666.m
Number of curves $4$
Conductor $1666$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1666.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1666.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1666.m1 1666l4 [1, 1, 1, -5538, 107309] [2] 3456  
1666.m2 1666l3 [1, 1, 1, -5048, 135925] [2] 1728  
1666.m3 1666l2 [1, 1, 1, -2108, -38123] [2] 1152  
1666.m4 1666l1 [1, 1, 1, -148, -491] [2] 576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1666.m have rank \(0\).

Modular form 1666.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 6q^{11} + 2q^{12} - 2q^{13} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.