Properties

Label 5520.bb
Number of curves $2$
Conductor $5520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5520.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.bb1 5520bg2 \([0, 1, 0, -3880, 91700]\) \(1577505447721/838350\) \(3433881600\) \([2]\) \(6912\) \(0.77950\)  
5520.bb2 5520bg1 \([0, 1, 0, -200, 1908]\) \(-217081801/285660\) \(-1170063360\) \([2]\) \(3456\) \(0.43292\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5520.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 5520.bb do not have complex multiplication.

Modular form 5520.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4q^{7} + q^{9} - 2q^{11} + 4q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.