Properties

Label 7098.bc
Number of curves $4$
Conductor $7098$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.bc1 7098y3 \([1, 0, 0, -13517, 603537]\) \(124318741396429/51631104\) \(113433535488\) \([2]\) \(12000\) \(1.0830\)  
7098.bc2 7098y4 \([1, 0, 0, -11437, 796145]\) \(-75306487574989/81352871712\) \(-178732259151264\) \([2]\) \(24000\) \(1.4296\)  
7098.bc3 7098y1 \([1, 0, 0, -452, -3732]\) \(4649101309/6804\) \(14948388\) \([2]\) \(2400\) \(0.27833\) \(\Gamma_0(N)\)-optimal
7098.bc4 7098y2 \([1, 0, 0, -322, -5890]\) \(-1680914269/5786802\) \(-12713603994\) \([2]\) \(4800\) \(0.62490\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7098.2.a.bc

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.