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Properties

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

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

Elliptic curves in class 5850.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bb1 5850bb2 \([1, -1, 0, -2549367, 1567376541]\) \(-6434774386429585/140608\) \(-40040325000000\) \([3]\) \(129600\) \(2.1364\)  
5850.bb2 5850bb1 \([1, -1, 0, -29367, 2456541]\) \(-9836106385/3407872\) \(-970444800000000\) \([]\) \(43200\) \(1.5871\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5850.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 5 q^{7} - q^{8} + 3 q^{11} + q^{13} - 5 q^{14} + q^{16} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.