Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("wz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.wz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.wz1 369600wz2 \([0, 1, 0, -3626257313, -22549816971297]\) \(160934676078320454012702173/86430430219822569086976\) \(2832152337443145943842029568000\) \([2]\) \(644087808\) \(4.5344\)  
369600.wz2 369600wz1 \([0, 1, 0, 869512287, -2763934961697]\) \(2218712073897830722499107/1384711926834951880704\) \(-45374240418527703226908672000\) \([2]\) \(322043904\) \(4.1878\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.wz

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