Properties

Label 42630.dh
Number of curves 2
Conductor 42630
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("42630.dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42630.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42630.dh1 42630dl2 [1, 0, 0, -2631210, 1642616100] [7] 1251264  
42630.dh2 42630dl1 [1, 0, 0, 7790, -325018] [] 178752 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42630.dh have rank \(0\).

Modular form 42630.2.a.dh

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} - 7q^{13} + q^{15} + q^{16} - 3q^{17} + q^{18} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.