Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.i3 369600i1 \([0, -1, 0, -58697233, -173071463663]\) \(87364831012240243408/1760913\) \(450793728000000\) \([2]\) \(23592960\) \(2.7953\) \(\Gamma_0(N)\)-optimal
369600.i2 369600i2 \([0, -1, 0, -58699233, -173059077663]\) \(21843440425782779332/3100814593569\) \(3175234143814656000000\) \([2, 2]\) \(47185920\) \(3.1419\)  
369600.i1 369600i3 \([0, -1, 0, -64023233, -139789401663]\) \(14171198121996897746/4077720290568771\) \(8351171155084843008000000\) \([2]\) \(94371840\) \(3.4884\)  
369600.i4 369600i4 \([0, -1, 0, -53407233, -205536081663]\) \(-8226100326647904626/4152140742401883\) \(-8503584240439056384000000\) \([2]\) \(94371840\) \(3.4884\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.