Properties

Label 1848.d
Number of curves 4
Conductor 1848
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1848.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1848.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1848.d1 1848b3 [0, -1, 0, -640232, -139597332] [2] 46080  
1848.d2 1848b2 [0, -1, 0, -586992, -172882980] [2, 2] 23040  
1848.d3 1848b1 [0, -1, 0, -586972, -172895372] [2] 11520 \(\Gamma_0(N)\)-optimal
1848.d4 1848b4 [0, -1, 0, -534072, -205375860] [2] 46080  

Rank

sage: E.rank()
 

The elliptic curves in class 1848.d have rank \(1\).

Modular form 1848.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{7} + q^{9} + q^{11} - 6q^{13} - 2q^{15} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.