Properties

Label 369600.jn
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("jn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.jn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.jn1 369600jn2 [0, -1, 0, -2679033, 31909386687] [] 57600000  
369600.jn2 369600jn1 [0, -1, 0, -894033, -380738313] [] 11520000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 369600.jn have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.jn do not have complex multiplication.

Modular form 369600.2.a.jn

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} + q^{11} - 6q^{13} + 7q^{17} - 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.