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Properties

Label 2842.b
Number of curves $2$
Conductor $2842$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2842.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2842.b1 2842d1 \([1, 1, 0, -711, -72827]\) \(-338608873/19120976\) \(-2249563705424\) \([]\) \(4608\) \(1.0500\) \(\Gamma_0(N)\)-optimal
2842.b2 2842d2 \([1, 1, 0, 6394, 1943572]\) \(245667233447/13974818816\) \(-1644123458883584\) \([]\) \(13824\) \(1.5993\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2842.b have rank \(1\).

Complex multiplication

The elliptic curves in class 2842.b do not have complex multiplication.

Modular form 2842.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + q^{13} - 3 q^{15} + q^{16} + 2 q^{18} + 4 q^{19} + O(q^{20})\) 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.