Properties

Label 100011.d
Number of curves 2
Conductor 100011
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("100011.d1")
sage: E.isogeny_class()

Elliptic curves in class 100011.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100011.d1 100011d1 [1, 0, 1, -692, 6941] 2 45312 \(\Gamma_0(N)\)-optimal
100011.d2 100011d2 [1, 0, 1, -647, 7895] 2 90624  

Rank

sage: E.rank()

The elliptic curves in class 100011.d have rank \(1\).

Modular form None

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

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 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.