Properties

Label 3192.k
Number of curves $2$
Conductor $3192$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 3192.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.k1 3192o1 \([0, 1, 0, -35, -66]\) \(304900096/96957\) \(1551312\) \([2]\) \(768\) \(-0.10828\) \(\Gamma_0(N)\)-optimal
3192.k2 3192o2 \([0, 1, 0, 100, -336]\) \(427694384/477603\) \(-122266368\) \([2]\) \(1536\) \(0.23829\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3192.k have rank \(1\).

Complex multiplication

The elliptic curves in class 3192.k do not have complex multiplication.

Modular form 3192.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.