Properties

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

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Show commands: SageMath
E = EllipticCurve("jb1")
 
E.isogeny_class()
 

Elliptic curves in class 369600.jb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.jb1 369600jb4 \([0, -1, 0, -920028033, -10740816612063]\) \(21026497979043461623321/161783881875\) \(662666780160000000000\) \([2]\) \(94371840\) \(3.5877\)  
369600.jb2 369600jb2 \([0, -1, 0, -57540033, -167576220063]\) \(5143681768032498601/14238434358225\) \(58320627131289600000000\) \([2, 2]\) \(47185920\) \(3.2412\)  
369600.jb3 369600jb3 \([0, -1, 0, -34860033, -301048020063]\) \(-1143792273008057401/8897444448004035\) \(-36443932459024527360000000\) \([2]\) \(94371840\) \(3.5877\)  
369600.jb4 369600jb1 \([0, -1, 0, -5052033, -296964063]\) \(3481467828171481/2005331497785\) \(8213837814927360000000\) \([2]\) \(23592960\) \(2.8946\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.jb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - q^{11} + 6 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.