Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ov1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600ov

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ov4 369600ov1 \([0, 1, 0, -7516993, 7930071743]\) \(1433528304665250149/162339408\) \(5319537721344000\) \([2]\) \(7372800\) \(2.4414\) \(\Gamma_0(N)\)-optimal
369600.ov3 369600ov2 \([0, 1, 0, -7536193, 7887505343]\) \(1444540994277943589/15251205665388\) \(499751507243433984000\) \([2]\) \(14745600\) \(2.7880\)  
369600.ov2 369600ov3 \([0, 1, 0, -27774593, -48029603457]\) \(72313087342699809269/11447096545640448\) \(375098459607546200064000\) \([2]\) \(36864000\) \(3.2462\)  
369600.ov1 369600ov4 \([0, 1, 0, -425905793, -3383174665857]\) \(260744057755293612689909/8504954620259328\) \(278690352996657659904000\) \([2]\) \(73728000\) \(3.5927\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.ov

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.