Properties

Label 1980b
Number of curves 4
Conductor 1980
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1980.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1980b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1980.a4 1980b1 [0, 0, 0, -408, -3107] [2] 864 \(\Gamma_0(N)\)-optimal
1980.a3 1980b2 [0, 0, 0, -903, 5902] [2] 1728  
1980.a2 1980b3 [0, 0, 0, -4008, 96433] [6] 2592  
1980.a1 1980b4 [0, 0, 0, -63903, 6217702] [6] 5184  

Rank

sage: E.rank()
 

The elliptic curves in class 1980b have rank \(0\).

Modular form 1980.2.a.a

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

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 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.