Properties

Label 10350bj
Number of curves $6$
Conductor $10350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("10350.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10350bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10350.bg5 10350bj1 [1, -1, 1, -94505, -12244503] [2] 73728 \(\Gamma_0(N)\)-optimal
10350.bg4 10350bj2 [1, -1, 1, -1552505, -744160503] [2, 2] 147456  
10350.bg1 10350bj3 [1, -1, 1, -24840005, -47645185503] [2] 294912  
10350.bg3 10350bj4 [1, -1, 1, -1593005, -703255503] [2, 2] 294912  
10350.bg2 10350bj5 [1, -1, 1, -5811755, 4620806997] [2] 589824  
10350.bg6 10350bj6 [1, -1, 1, 1977745, -3409884003] [2] 589824  

Rank

sage: E.rank()
 

The elliptic curves in class 10350bj have rank \(1\).

Modular form 10350.2.a.bg

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 4q^{11} + 2q^{13} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.