Properties

Label 37030.s
Number of curves $4$
Conductor $37030$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("37030.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37030.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37030.s1 37030t4 [1, -1, 1, -141607, 20544781] [2] 202752  
37030.s2 37030t3 [1, -1, 1, -46387, -3581851] [2] 202752  
37030.s3 37030t2 [1, -1, 1, -9357, 284081] [2, 2] 101376  
37030.s4 37030t1 [1, -1, 1, 1223, 25929] [2] 50688 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37030.s have rank \(1\).

Modular form 37030.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} - 3q^{9} + q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.