Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 7098.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.p1 7098p1 \([1, 0, 1, -11782, -493192]\) \(-82318551880501/54432\) \(-119587104\) \([]\) \(12000\) \(0.86692\) \(\Gamma_0(N)\)-optimal
7098.p2 7098p2 \([1, 0, 1, 24293, -2543578]\) \(721710134999099/1691848015872\) \(-3716990090870784\) \([]\) \(60000\) \(1.6716\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7098.2.a.p

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.