Properties

Label 188760.bl
Number of curves $2$
Conductor $188760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 188760.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bl1 188760y2 \([0, -1, 0, -1389120, 604809900]\) \(61387394182/2851875\) \(13771923601962240000\) \([2]\) \(3446784\) \(2.4337\)  
188760.bl2 188760y1 \([0, -1, 0, 48360, 36142812]\) \(5180116/236925\) \(-572064518850739200\) \([2]\) \(1723392\) \(2.0871\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.bl have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.bl do not have complex multiplication.

Modular form 188760.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + q^{13} - q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.