Properties

Label 7098.n
Number of curves $2$
Conductor $7098$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.n1 7098i2 \([1, 0, 1, -620989828, -5956328145220]\) \(-5486773802537974663600129/2635437714\) \(-12720754476874626\) \([]\) \(1382976\) \(3.3290\)  
7098.n2 7098i1 \([1, 0, 1, 120662, -182269540]\) \(40251338884511/2997011332224\) \(-14466001271480793216\) \([]\) \(197568\) \(2.3561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7098.n have rank \(0\).

Complex multiplication

The elliptic curves in class 7098.n do not have complex multiplication.

Modular form 7098.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 5q^{11} + q^{12} + q^{14} + q^{15} + q^{16} - 3q^{17} - q^{18} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.