Properties

Label 3920.h
Number of curves $4$
Conductor $3920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3920.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.h1 3920bf3 \([0, 1, 0, -2025, -35750]\) \(488095744/125\) \(235298000\) \([2]\) \(2160\) \(0.59231\)  
3920.h2 3920bf4 \([0, 1, 0, -1780, -44472]\) \(-20720464/15625\) \(-470596000000\) \([2]\) \(4320\) \(0.93888\)  
3920.h3 3920bf1 \([0, 1, 0, -65, 118]\) \(16384/5\) \(9411920\) \([2]\) \(720\) \(0.043005\) \(\Gamma_0(N)\)-optimal
3920.h4 3920bf2 \([0, 1, 0, 180, 1000]\) \(21296/25\) \(-752953600\) \([2]\) \(1440\) \(0.38958\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3920.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3920.h do not have complex multiplication.

Modular form 3920.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{5} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.