Properties

Label 7800.n
Number of curves $4$
Conductor $7800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.n1 7800u3 \([0, 1, 0, -7608, -251712]\) \(3044193988/85293\) \(1364688000000\) \([2]\) \(16384\) \(1.1076\)  
7800.n2 7800u2 \([0, 1, 0, -1108, 8288]\) \(37642192/13689\) \(54756000000\) \([2, 2]\) \(8192\) \(0.76098\)  
7800.n3 7800u1 \([0, 1, 0, -983, 11538]\) \(420616192/117\) \(29250000\) \([2]\) \(4096\) \(0.41441\) \(\Gamma_0(N)\)-optimal
7800.n4 7800u4 \([0, 1, 0, 3392, 62288]\) \(269676572/257049\) \(-4112784000000\) \([2]\) \(16384\) \(1.1076\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7800.n have rank \(1\).

Complex multiplication

The elliptic curves in class 7800.n do not have complex multiplication.

Modular form 7800.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{7} + q^{9} - q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.