Properties

Label 26450.i
Number of curves $4$
Conductor $26450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 26450.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26450.i1 26450i2 \([1, 0, 1, -66401, 6580348]\) \(-349938025/8\) \(-740179445000\) \([]\) \(71280\) \(1.3910\)  
26450.i2 26450i3 \([1, 0, 1, -39951, -3708702]\) \(-121945/32\) \(-1850448612500000\) \([]\) \(118800\) \(1.6464\)  
26450.i3 26450i1 \([1, 0, 1, -276, 20748]\) \(-25/2\) \(-185044861250\) \([]\) \(23760\) \(0.84165\) \(\Gamma_0(N)\)-optimal
26450.i4 26450i4 \([1, 0, 1, 290674, 27370048]\) \(46969655/32768\) \(-1894859379200000000\) \([]\) \(356400\) \(2.1957\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26450.i have rank \(1\).

Complex multiplication

The elliptic curves in class 26450.i do not have complex multiplication.

Modular form 26450.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2 q^{7} - q^{8} - 2 q^{9} + 3 q^{11} + q^{12} - 4 q^{13} + 2 q^{14} + q^{16} + 3 q^{17} + 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.