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Properties

Label 2450.x
Number of curves $2$
Conductor $2450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 2450.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.x1 2450bf2 \([1, 1, 1, -55763, 7098531]\) \(-417267265/235298\) \(-10813505625781250\) \([]\) \(17280\) \(1.7798\)  
2450.x2 2450bf1 \([1, 1, 1, 5487, -128969]\) \(397535/392\) \(-18015003125000\) \([]\) \(5760\) \(1.2305\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2450.x do not have complex multiplication.

Modular form 2450.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} - 2 q^{9} + 3 q^{11} - q^{12} - 2 q^{13} + q^{16} - 3 q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})\) 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.