Properties

Label 29645.h
Number of curves $4$
Conductor $29645$
CM no
Rank $1$
Graph

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

Elliptic curves in class 29645.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.h1 29645d4 \([1, -1, 0, -60871190, 182810845531]\) \(119678115308998401/1925\) \(401213081671325\) \([2]\) \(1474560\) \(2.8008\)  
29645.h2 29645d3 \([1, -1, 0, -4130660, 2338524425]\) \(37397086385121/10316796875\) \(2150251359582257421875\) \([2]\) \(1474560\) \(2.8008\)  
29645.h3 29645d2 \([1, -1, 0, -3804565, 2856950256]\) \(29220958012401/3705625\) \(772335182217300625\) \([2, 2]\) \(737280\) \(2.4542\)  
29645.h4 29645d1 \([1, -1, 0, -217520, 52598475]\) \(-5461074081/2562175\) \(-534014611704533575\) \([2]\) \(368640\) \(2.1077\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29645.h have rank \(1\).

Complex multiplication

The elliptic curves in class 29645.h do not have complex multiplication.

Modular form 29645.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.