Properties

Label 142956.l
Number of curves 2
Conductor 142956
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("142956.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142956.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142956.l1 142956i2 [0, 0, 0, -40071, -1467826] [2] 628992  
142956.l2 142956i1 [0, 0, 0, 8664, -171475] [2] 314496 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 142956.l have rank \(0\).

Modular form 142956.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{7} - q^{11} + 2q^{13} - 4q^{17} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.