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Properties

Label 22253.h
Number of curves $2$
Conductor $22253$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 22253.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22253.h1 22253e2 \([1, 0, 1, -14890, 644301]\) \(15124197817/1294139\) \(31237369408091\) \([2]\) \(59136\) \(1.3306\)  
22253.h2 22253e1 \([1, 0, 1, 1005, 46649]\) \(4657463/41503\) \(-1001781526207\) \([2]\) \(29568\) \(0.98401\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22253.h have rank \(0\).

Complex multiplication

The elliptic curves in class 22253.h do not have complex multiplication.

Modular form 22253.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 2 q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - q^{16} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.