Properties

Label 282576i
Number of curves $6$
Conductor $282576$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("282576.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 282576i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
282576.i5 282576i1 [0, -1, 0, -10549784, -14117680080] [2] 20643840 \(\Gamma_0(N)\)-optimal
282576.i4 282576i2 [0, -1, 0, -172089064, -868854318416] [2, 2] 41287680  
282576.i3 282576i3 [0, -1, 0, -175385784, -833829965136] [2, 2] 82575360  
282576.i1 282576i4 [0, -1, 0, -2753420824, -55609608153680] [2] 82575360  
282576.i2 282576i5 [0, -1, 0, -571463144, 4274617393200] [2] 165150720  
282576.i6 282576i6 [0, -1, 0, 167944056, -3700771461072] [2] 165150720  

Rank

sage: E.rank()
 

The elliptic curves in class 282576i have rank \(0\).

Modular form 282576.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.