Properties

Label 36784bh
Number of curves $3$
Conductor $36784$
CM no
Rank $2$
Graph

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

Elliptic curves in class 36784bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36784.j2 36784bh1 \([0, -1, 0, -30048, 2015488]\) \(-413493625/152\) \(-1102959706112\) \([]\) \(51840\) \(1.2787\) \(\Gamma_0(N)\)-optimal
36784.j3 36784bh2 \([0, -1, 0, 18352, 7614400]\) \(94196375/3511808\) \(-25482781050011648\) \([]\) \(155520\) \(1.8280\)  
36784.j1 36784bh3 \([0, -1, 0, -165568, -208528384]\) \(-69173457625/2550136832\) \(-18504593228737544192\) \([]\) \(466560\) \(2.3773\)  

Rank

sage: E.rank()
 

The elliptic curves in class 36784bh have rank \(2\).

Complex multiplication

The elliptic curves in class 36784bh do not have complex multiplication.

Modular form 36784.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} - 2 q^{9} - 5 q^{13} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.