Properties

Label 2898.j
Number of curves $2$
Conductor $2898$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2898.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.j1 2898j2 \([1, -1, 0, -243, 6723]\) \(-2181825073/25039686\) \(-18253931094\) \([3]\) \(2880\) \(0.65091\)  
2898.j2 2898j1 \([1, -1, 0, 27, -243]\) \(2924207/34776\) \(-25351704\) \([]\) \(960\) \(0.10160\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2898.j do not have complex multiplication.

Modular form 2898.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3q^{5} + q^{7} - q^{8} - 3q^{10} + 5q^{13} - q^{14} + q^{16} + 8q^{19} + O(q^{20})\)  Toggle raw display

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.