Properties

Label 158400.bc
Number of curves 4
Conductor 158400
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("158400.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 158400.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.bc1 158400cc4 [0, 0, 0, -6390300, -6217702000] [2] 3981312  
158400.bc2 158400cc3 [0, 0, 0, -400800, -96433000] [2] 1990656  
158400.bc3 158400cc2 [0, 0, 0, -90300, -5902000] [2] 1327104  
158400.bc4 158400cc1 [0, 0, 0, -40800, 3107000] [2] 663552 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 158400.bc have rank \(2\).

Modular form 158400.2.a.bc

sage: E.q_eigenform(10)
 
\( q - 4q^{7} + q^{11} - 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.