Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.v1 369600v1 \([0, -1, 0, -153281633, -293323828863]\) \(388950302854250851396/188776686710390625\) \(193307327191440000000000000\) \([2]\) \(113541120\) \(3.7374\) \(\Gamma_0(N)\)-optimal
369600.v2 369600v2 \([0, -1, 0, 555306367, -2241232240863]\) \(9246805402538461809742/6410550311279296875\) \(-13128807037500000000000000000\) \([2]\) \(227082240\) \(4.0839\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.v

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