Properties

Label 52800.d
Number of curves 4
Conductor 52800
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("52800.d1")
sage: E.isogeny_class()

Elliptic curves in class 52800.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
52800.d1 52800v4 [0, -1, 0, -234433, 43724737] 2 393216  
52800.d2 52800v2 [0, -1, 0, -18433, 308737] 4 196608  
52800.d3 52800v1 [0, -1, 0, -10433, -403263] 2 98304 \(\Gamma_0(N)\)-optimal
52800.d4 52800v3 [0, -1, 0, 69567, 2332737] 2 393216  

Rank

sage: E.rank()

The elliptic curves in class 52800.d have rank \(1\).

Modular form 52800.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.