Properties

Label 185020m
Number of curves 4
Conductor 185020
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("185020.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 185020m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185020.o4 185020m1 [0, -1, 0, -38125, 2819250] [2] 870912 \(\Gamma_0(N)\)-optimal
185020.o3 185020m2 [0, -1, 0, -84380, -5303128] [2] 1741824  
185020.o2 185020m3 [0, -1, 0, -374525, -86982730] [2] 2612736  
185020.o1 185020m4 [0, -1, 0, -5971380, -5614436728] [2] 5225472  

Rank

sage: E.rank()
 

The elliptic curves in class 185020m have rank \(2\).

Modular form 185020.2.a.o

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.