Properties

Label 107712.dh
Number of curves $4$
Conductor $107712$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 107712.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
107712.dh1 107712dv4 \([0, 0, 0, -278749164, 1791261643088]\) \(12534210458299016895673/315581882565708\) \(60308636929989314347008\) \([2]\) \(23592960\) \(3.4793\)  
107712.dh2 107712dv2 \([0, 0, 0, -18086124, 25738740560]\) \(3423676911662954233/483711578981136\) \(92438722268954137460736\) \([2, 2]\) \(11796480\) \(3.1327\)  
107712.dh3 107712dv1 \([0, 0, 0, -4769004, -3606865072]\) \(62768149033310713/6915442583808\) \(1321561658122838212608\) \([2]\) \(5898240\) \(2.7861\) \(\Gamma_0(N)\)-optimal
107712.dh4 107712dv3 \([0, 0, 0, 29502996, 138334598480]\) \(14861225463775641287/51859390496937804\) \(-9910483857510933231304704\) \([2]\) \(23592960\) \(3.4793\)  

Rank

sage: E.rank()
 

The elliptic curves in class 107712.dh have rank \(0\).

Complex multiplication

The elliptic curves in class 107712.dh do not have complex multiplication.

Modular form 107712.2.a.dh

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} - q^{11} - 6 q^{13} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.