Properties

Label 7920.c
Number of curves $4$
Conductor $7920$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 7920.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7920.c1 7920j3 \([0, 0, 0, -95043, -11277902]\) \(127191074376964/495\) \(369515520\) \([2]\) \(16384\) \(1.2801\)  
7920.c2 7920j2 \([0, 0, 0, -5943, -176042]\) \(124386546256/245025\) \(45727545600\) \([2, 2]\) \(8192\) \(0.93355\)  
7920.c3 7920j4 \([0, 0, 0, -3963, -295238]\) \(-9220796644/45106875\) \(-33672101760000\) \([2]\) \(16384\) \(1.2801\)  
7920.c4 7920j1 \([0, 0, 0, -498, -713]\) \(1171019776/658845\) \(7684768080\) \([2]\) \(4096\) \(0.58698\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7920.c have rank \(1\).

Complex multiplication

The elliptic curves in class 7920.c do not have complex multiplication.

Modular form 7920.2.a.c

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