Properties

Label 44180.c
Number of curves 4
Conductor 44180
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("44180.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44180.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44180.c1 44180g3 [0, 1, 0, -91305, 10586428] [2] 156492  
44180.c2 44180g4 [0, 1, 0, -80260, 13254900] [2] 312984  
44180.c3 44180g1 [0, 1, 0, -2945, -43280] [2] 52164 \(\Gamma_0(N)\)-optimal
44180.c4 44180g2 [0, 1, 0, 8100, -281852] [2] 104328  

Rank

sage: E.rank()
 

The elliptic curves in class 44180.c have rank \(0\).

Modular form 44180.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.