Properties

Label 7938.n
Number of curves $2$
Conductor $7938$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7938.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7938.n1 7938g1 \([1, -1, 0, -303, -2143]\) \(-35937/4\) \(-343064484\) \([]\) \(3456\) \(0.37515\) \(\Gamma_0(N)\)-optimal
7938.n2 7938g2 \([1, -1, 0, 1902, 2708]\) \(109503/64\) \(-444611571264\) \([]\) \(10368\) \(0.92445\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7938.n have rank \(0\).

Complex multiplication

The elliptic curves in class 7938.n do not have complex multiplication.

Modular form 7938.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} + q^{13} + q^{16} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.