Properties

Label 2450y
Number of curves 6
Conductor 2450
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2450.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2450y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2450.t5 2450y1 [1, 0, 0, -638, -12608] [2] 2304 \(\Gamma_0(N)\)-optimal
2450.t4 2450y2 [1, 0, 0, -12888, -563858] [2] 4608  
2450.t6 2450y3 [1, 0, 0, 5487, 263017] [2] 6912  
2450.t3 2450y4 [1, 0, 0, -43513, 2860017] [2] 13824  
2450.t2 2450y5 [1, 0, 0, -208888, 36835392] [2] 20736  
2450.t1 2450y6 [1, 0, 0, -3344888, 2354339392] [2] 41472  

Rank

sage: E.rank()
 

The elliptic curves in class 2450y have rank \(1\).

Modular form 2450.2.a.t

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.