Properties

Label 52800hf
Number of curves 4
Conductor 52800
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("52800.hs1")
sage: E.isogeny_class()

Elliptic curves in class 52800hf

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
52800.hs3 52800hf1 [0, 1, 0, -10433, 403263] 2 98304 \(\Gamma_0(N)\)-optimal
52800.hs2 52800hf2 [0, 1, 0, -18433, -308737] 4 196608  
52800.hs4 52800hf3 [0, 1, 0, 69567, -2332737] 2 393216  
52800.hs1 52800hf4 [0, 1, 0, -234433, -43724737] 2 393216  

Rank

sage: E.rank()

The elliptic curves in class 52800hf have rank \(0\).

Modular form 52800.2.a.hs

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 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.