Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("nz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.nz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.nz1 369600nz2 \([0, 1, 0, -2073, -37017]\) \(1925134784/693\) \(354816000\) \([2]\) \(229376\) \(0.60951\)  
369600.nz2 369600nz1 \([0, 1, 0, -148, -442]\) \(45118016/17787\) \(142296000\) \([2]\) \(114688\) \(0.26293\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.nz

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.