Properties

Label 112518.bi
Number of curves $2$
Conductor $112518$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 112518.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112518.bi1 112518be1 \([1, -1, 1, -2909, -59327]\) \(3733252610697/23278724\) \(16970189796\) \([2]\) \(107520\) \(0.80071\) \(\Gamma_0(N)\)-optimal
112518.bi2 112518be2 \([1, -1, 1, -1199, -129779]\) \(-261284780457/9875692358\) \(-7199379728982\) \([2]\) \(215040\) \(1.1473\)  

Rank

sage: E.rank()
 

The elliptic curves in class 112518.bi have rank \(0\).

Complex multiplication

The elliptic curves in class 112518.bi do not have complex multiplication.

Modular form 112518.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} + q^{7} + q^{8} + 2 q^{10} + 2 q^{11} - 6 q^{13} + q^{14} + q^{16} - 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.