Properties

Label 100016p
Number of curves 4
Conductor 100016
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100016.h1")
sage: E.isogeny_class()

Elliptic curves in class 100016p

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.h3 100016p1 [0, 0, 0, -39611, -3034390] 2 113664 \(\Gamma_0(N)\)-optimal
100016.h2 100016p2 [0, 0, 0, -39931, -2982870] 4 227328  
100016.h4 100016p3 [0, 0, 0, 12709, -10278774] 2 454656  
100016.h1 100016p4 [0, 0, 0, -97691, 7610314] 4 454656  

Rank

sage: E.rank()

The elliptic curves in class 100016p have rank \(1\).

Modular form 100016.2.a.h

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.