Properties

Label 2898i
Number of curves $6$
Conductor $2898$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2898.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2898i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2898.i5 2898i1 [1, -1, 0, 1134, -30380] [2] 4096 \(\Gamma_0(N)\)-optimal
2898.i4 2898i2 [1, -1, 0, -10386, -346028] [2, 2] 8192  
2898.i2 2898i3 [1, -1, 0, -159426, -24460700] [2] 16384  
2898.i3 2898i4 [1, -1, 0, -45666, 3428932] [2, 2] 16384  
2898.i1 2898i5 [1, -1, 0, -712206, 231518920] [2] 32768  
2898.i6 2898i6 [1, -1, 0, 56394, 16513024] [2] 32768  

Rank

sage: E.rank()
 

The elliptic curves in class 2898i have rank \(0\).

Modular form 2898.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 2q^{5} + q^{7} - q^{8} - 2q^{10} + 4q^{11} - 2q^{13} - q^{14} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.