Properties

Label 3850d
Number of curves 4
Conductor 3850
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3850.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3850.k3 3850d1 [1, 1, 0, -1400, 392000] [2] 13824 \(\Gamma_0(N)\)-optimal
3850.k2 3850d2 [1, 1, 0, -89400, 10160000] [2] 27648  
3850.k4 3850d3 [1, 1, 0, 12600, -10570000] [2] 41472  
3850.k1 3850d4 [1, 1, 0, -652900, -197575500] [2] 82944  

Rank

sage: E.rank()
 

The elliptic curves in class 3850d have rank \(1\).

Modular form 3850.2.a.k

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.