Properties

Label 2450.l
Number of curves $4$
Conductor $2450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2450.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2450.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2450.l1 2450e4 [1, -1, 0, -327917, 72354491] [2] 18432  
2450.l2 2450e3 [1, -1, 0, -107417, -12636009] [2] 18432  
2450.l3 2450e2 [1, -1, 0, -21667, 998241] [2, 2] 9216  
2450.l4 2450e1 [1, -1, 0, 2833, 91741] [2] 4608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2450.l have rank \(0\).

Modular form 2450.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 3q^{9} + 4q^{11} - 6q^{13} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.