Properties

Label 369600ij
Number of curves $4$
Conductor $369600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ij1")
 
E.isogeny_class()
 

Elliptic curves in class 369600ij

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ij4 369600ij1 \([0, -1, 0, 123167, -9934463]\) \(50447927375/39517632\) \(-161864220672000000\) \([2]\) \(2654208\) \(1.9901\) \(\Gamma_0(N)\)-optimal
369600.ij3 369600ij2 \([0, -1, 0, -580833, -85262463]\) \(5290763640625/2291573592\) \(9386285432832000000\) \([2]\) \(5308416\) \(2.3367\)  
369600.ij2 369600ij3 \([0, -1, 0, -1316833, 739153537]\) \(-61653281712625/21875235228\) \(-89600963493888000000\) \([2]\) \(7962624\) \(2.5394\)  
369600.ij1 369600ij4 \([0, -1, 0, -22612833, 41393217537]\) \(312196988566716625/25367712678\) \(103906151129088000000\) \([2]\) \(15925248\) \(2.8860\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600ij have rank \(1\).

Complex multiplication

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

Modular form 369600.2.a.ij

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - q^{11} + 2 q^{13} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.