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Properties

Label 112710bs
Number of curves $2$
Conductor $112710$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 112710bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.bs1 112710bs1 \([1, 1, 1, -190003056, 1007986873809]\) \(31427652507069423952801/654426190080\) \(15796257318463115520\) \([2]\) \(14008320\) \(3.2132\) \(\Gamma_0(N)\)-optimal
112710.bs2 112710bs2 \([1, 1, 1, -189794976, 1010305051473]\) \(-31324512477868037557921/143427974919699600\) \(-3462002641154518554272400\) \([2]\) \(28016640\) \(3.5598\)  

Rank

sage: E.rank()
 

The elliptic curves in class 112710bs have rank \(0\).

Complex multiplication

The elliptic curves in class 112710bs do not have complex multiplication.

Modular form 112710.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - 2 q^{14} + q^{15} + q^{16} + q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.