Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.bb1 7098ba2 \([1, 0, 0, -5158, -143014]\) \(531373116625/2058\) \(58778538\) \([]\) \(6048\) \(0.70410\)  
7098.bb2 7098ba1 \([1, 0, 0, -88, -40]\) \(2640625/1512\) \(43184232\) \([3]\) \(2016\) \(0.15479\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7098.2.a.bb

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