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Properties

Label 5550b
Number of curves $2$
Conductor $5550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 5550b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.g2 5550b1 \([1, 1, 0, -2084900, -1546878000]\) \(-64144540676215729729/28962038218752000\) \(-452531847168000000000\) \([]\) \(190080\) \(2.6701\) \(\Gamma_0(N)\)-optimal
5550.g1 5550b2 \([1, 1, 0, -184100900, -961538430000]\) \(-44164307457093068844199489/1823508000000000\) \(-28492312500000000000\) \([]\) \(570240\) \(3.2195\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5550b have rank \(1\).

Complex multiplication

The elliptic curves in class 5550b do not have complex multiplication.

Modular form 5550.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} - 2 q^{13} - q^{14} + q^{16} - 3 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.