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Properties

Label 2873b
Number of curves $2$
Conductor $2873$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2873b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2873.b2 2873b1 \([1, -1, 0, -123824, 16774499]\) \(43499078731809/82055753\) \(396067447082177\) \([2]\) \(20160\) \(1.6911\) \(\Gamma_0(N)\)-optimal
2873.b1 2873b2 \([1, -1, 0, -1980289, 1073103084]\) \(177930109857804849/634933\) \(3064700318797\) \([2]\) \(40320\) \(2.0376\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2873b have rank \(0\).

Complex multiplication

The elliptic curves in class 2873b do not have complex multiplication.

Modular form 2873.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{5} + 2 q^{7} - 3 q^{8} - 3 q^{9} - 4 q^{10} - 6 q^{11} + 2 q^{14} - q^{16} + q^{17} - 3 q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.