Properties

Label 1100b
Number of curves 4
Conductor 1100
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1100.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1100b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1100.e4 1100b1 [0, -1, 0, -1133, 14762] [2] 864 \(\Gamma_0(N)\)-optimal
1100.e3 1100b2 [0, -1, 0, -2508, -26488] [2] 1728  
1100.e2 1100b3 [0, -1, 0, -11133, -442738] [2] 2592  
1100.e1 1100b4 [0, -1, 0, -177508, -28726488] [2] 5184  

Rank

sage: E.rank()
 

The elliptic curves in class 1100b have rank \(0\).

Modular form 1100.2.a.e

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + 4q^{7} + q^{9} - q^{11} + 4q^{13} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.