Properties

Label 61347.s
Number of curves 2
Conductor 61347
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("61347.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61347.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.s1 61347w1 [0, 1, 1, -12393, -540952] [] 80640 \(\Gamma_0(N)\)-optimal
61347.s2 61347w2 [0, 1, 1, 43377, -2721559] [] 241920  

Rank

sage: E.rank()
 

The elliptic curves in class 61347.s have rank \(1\).

Modular form 61347.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{4} - q^{7} + q^{9} - 2q^{12} + 4q^{16} - 6q^{17} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.