Properties

Label 5850.bi
Number of curves $2$
Conductor $5850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5850.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bi1 5850br2 \([1, -1, 1, -10355, 365897]\) \(10779215329/1232010\) \(14033363906250\) \([2]\) \(18432\) \(1.2550\)  
5850.bi2 5850br1 \([1, -1, 1, 895, 28397]\) \(6967871/35100\) \(-399810937500\) \([2]\) \(9216\) \(0.90841\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.bi have rank \(0\).

Complex multiplication

The elliptic curves in class 5850.bi do not have complex multiplication.

Modular form 5850.2.a.bi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.