Properties

Label 27753d
Number of curves 4
Conductor 27753
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("27753.c1")
sage: E.isogeny_class()

Elliptic curves in class 27753d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
27753.c3 27753d1 [1, 0, 0, -5484, -155457] 2 36288 \(\Gamma_0(N)\)-optimal
27753.c2 27753d2 [1, 0, 0, -9689, 114504] 4 72576  
27753.c4 27753d3 [1, 0, 0, 36566, 900839] 2 145152  
27753.c1 27753d4 [1, 0, 0, -123224, 16622493] 2 145152  

Rank

sage: E.rank()

The elliptic curves in class 27753d have rank \(0\).

Modular form 27753.2.a.c

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

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.