Properties

Label 369600.x
Number of curves $2$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.x1 369600x2 \([0, -1, 0, -91833, 5556537]\) \(10706185664/4546773\) \(36374184000000000\) \([2]\) \(3686400\) \(1.8744\)  
369600.x2 369600x1 \([0, -1, 0, -43708, -3442838]\) \(73876521536/1440747\) \(180093375000000\) \([2]\) \(1843200\) \(1.5278\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 4 q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.