Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3920.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.t1 3920ba3 \([0, 0, 0, -209867, -37003526]\) \(2121328796049/120050\) \(57850930995200\) \([2]\) \(18432\) \(1.7051\)  
3920.t2 3920ba4 \([0, 0, 0, -68747, 6483386]\) \(74565301329/5468750\) \(2635337600000000\) \([4]\) \(18432\) \(1.7051\)  
3920.t3 3920ba2 \([0, 0, 0, -13867, -508326]\) \(611960049/122500\) \(59031562240000\) \([2, 2]\) \(9216\) \(1.3585\)  
3920.t4 3920ba1 \([0, 0, 0, 1813, -47334]\) \(1367631/2800\) \(-1349292851200\) \([2]\) \(4608\) \(1.0119\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3920.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})\)  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.