Properties

Label 203280j
Number of curves $6$
Conductor $203280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.hb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.hb6 203280j1 [0, 1, 0, 19320, -1440012] [2] 983040 \(\Gamma_0(N)\)-optimal
203280.hb5 203280j2 [0, 1, 0, -135560, -15007500] [2, 2] 1966080  
203280.hb4 203280j3 [0, 1, 0, -716360, 220332660] [2] 3932160  
203280.hb2 203280j4 [0, 1, 0, -2032840, -1116188812] [2, 2] 3932160  
203280.hb3 203280j5 [0, 1, 0, -1897320, -1271277900] [2] 7864320  
203280.hb1 203280j6 [0, 1, 0, -32524840, -71406347212] [2] 7864320  

Rank

sage: E.rank()
 

The elliptic curves in class 203280j have rank \(0\).

Modular form 203280.2.a.hb

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{7} + q^{9} + 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.