Properties

Label 21780n
Number of curves 4
Conductor 21780
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("21780.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 21780n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21780.l4 21780n1 [0, 0, 0, -49368, 4135417] [2] 103680 \(\Gamma_0(N)\)-optimal
21780.l3 21780n2 [0, 0, 0, -109263, -7855562] [2] 207360  
21780.l2 21780n3 [0, 0, 0, -484968, -128352323] [2] 311040  
21780.l1 21780n4 [0, 0, 0, -7732263, -8275761362] [2] 622080  

Rank

sage: E.rank()
 

The elliptic curves in class 21780n have rank \(0\).

Modular form 21780.2.a.l

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

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.