Properties

Label 19600.bv
Number of curves 4
Conductor 19600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19600.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bv1 19600i3 [0, 0, 0, -131075, -18264750] [2] 55296  
19600.bv2 19600i2 [0, 0, 0, -8575, -257250] [2, 2] 27648  
19600.bv3 19600i1 [0, 0, 0, -2450, 42875] [2] 13824 \(\Gamma_0(N)\)-optimal
19600.bv4 19600i4 [0, 0, 0, 15925, -1457750] [2] 55296  

Rank

sage: E.rank()
 

The elliptic curves in class 19600.bv have rank \(0\).

Modular form 19600.2.a.bv

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.