Properties

Label 3648.bc
Number of curves $4$
Conductor $3648$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3648.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.bc1 3648bh3 \([0, 1, 0, -27393, 1735935]\) \(8671983378625/82308\) \(21576548352\) \([2]\) \(6912\) \(1.1452\)  
3648.bc2 3648bh4 \([0, 1, 0, -26753, 1821567]\) \(-8078253774625/846825858\) \(-221990317719552\) \([2]\) \(13824\) \(1.4918\)  
3648.bc3 3648bh1 \([0, 1, 0, -513, -513]\) \(57066625/32832\) \(8606711808\) \([2]\) \(2304\) \(0.59592\) \(\Gamma_0(N)\)-optimal
3648.bc4 3648bh2 \([0, 1, 0, 2047, -2049]\) \(3616805375/2105352\) \(-551905394688\) \([2]\) \(4608\) \(0.94249\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3648.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 3648.bc do not have complex multiplication.

Modular form 3648.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4q^{7} + q^{9} + 4q^{13} + 6q^{17} + q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.