Properties

Label 11760bh
Number of curves $4$
Conductor $11760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 11760bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11760.cr3 11760bh1 \([0, 1, 0, -3495, -77400]\) \(2508888064/118125\) \(222356610000\) \([2]\) \(18432\) \(0.93809\) \(\Gamma_0(N)\)-optimal
11760.cr2 11760bh2 \([0, 1, 0, -9620, 260700]\) \(3269383504/893025\) \(26896255545600\) \([2, 2]\) \(36864\) \(1.2847\)  
11760.cr1 11760bh3 \([0, 1, 0, -141920, 20529060]\) \(2624033547076/324135\) \(39049378421760\) \([2]\) \(73728\) \(1.6312\)  
11760.cr4 11760bh4 \([0, 1, 0, 24680, 1728740]\) \(13799183324/18600435\) \(-2240842319170560\) \([4]\) \(73728\) \(1.6312\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11760bh have rank \(0\).

Complex multiplication

The elliptic curves in class 11760bh do not have complex multiplication.

Modular form 11760.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 4 q^{11} + 6 q^{13} + q^{15} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.