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Properties

Label 1922.c
Number of curves $2$
Conductor $1922$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1922.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1922.c1 1922e2 \([1, -1, 1, -76332, 8136267]\) \(51181724570498001/4\) \(3844\) \([]\) \(5880\) \(1.0529\)  
1922.c2 1922e1 \([1, -1, 1, -72, -117]\) \(42396561/16384\) \(15745024\) \([]\) \(840\) \(0.079973\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1922.c have rank \(1\).

Complex multiplication

The elliptic curves in class 1922.c do not have complex multiplication.

Modular form 1922.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} - 3 q^{7} + q^{8} + 6 q^{9} + q^{10} + 3 q^{11} - 3 q^{12} - 5 q^{13} - 3 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.