Properties

Label 192027p
Number of curves 2
Conductor 192027
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("192027.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 192027p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
192027.l2 192027p1 [1, 1, 0, -1473540, -10012407093] [2] 10137600 \(\Gamma_0(N)\)-optimal
192027.l1 192027p2 [1, 1, 0, -79244475, -269440692066] [2] 20275200  

Rank

sage: E.rank()
 

The elliptic curves in class 192027p have rank \(1\).

Modular form 192027.2.a.l

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

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.