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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 3192l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.j1 3192l1 \([0, -1, 0, -152, 732]\) \(381775972/25137\) \(25740288\) \([2]\) \(1152\) \(0.17157\) \(\Gamma_0(N)\)-optimal
3192.j2 3192l2 \([0, -1, 0, 128, 2860]\) \(112363774/1842183\) \(-3772790784\) \([2]\) \(2304\) \(0.51814\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3192.2.a.l

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