Properties

Label 2112m
Number of curves 4
Conductor 2112
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2112.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2112m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.s3 2112m1 [0, 1, 0, -49, -145] [2] 256 \(\Gamma_0(N)\)-optimal
2112.s2 2112m2 [0, 1, 0, -129, 351] [2, 2] 512  
2112.s1 2112m3 [0, 1, 0, -1889, 30975] [4] 1024  
2112.s4 2112m4 [0, 1, 0, 351, 2751] [2] 1024  

Rank

sage: E.rank()
 

The elliptic curves in class 2112m have rank \(0\).

Modular form 2112.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{9} - q^{11} - 2q^{13} - 2q^{15} + 6q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.