Properties

Label 7938.s
Number of curves $2$
Conductor $7938$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7938.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7938.s1 7938ba2 \([1, -1, 1, -2729, 60589]\) \(-35937/4\) \(-250094008836\) \([]\) \(10368\) \(0.92445\)  
7938.s2 7938ba1 \([1, -1, 1, 211, -171]\) \(109503/64\) \(-609892416\) \([]\) \(3456\) \(0.37515\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7938.s have rank \(1\).

Complex multiplication

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

Modular form 7938.2.a.s

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.