Properties

Label 58800.m
Number of curves 6
Conductor 58800
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("58800.m1")
sage: E.isogeny_class()

Elliptic curves in class 58800.m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
58800.m1 58800gb6 [0, -1, 0, -15366808, -23180759888] 2 1572864  
58800.m2 58800gb4 [0, -1, 0, -960808, -361655888] 4 786432  
58800.m3 58800gb3 [0, -1, 0, -764808, 256136112] 2 786432  
58800.m4 58800gb5 [0, -1, 0, -666808, -587447888] 2 1572864  
58800.m5 58800gb2 [0, -1, 0, -78808, -1799888] 4 393216  
58800.m6 58800gb1 [0, -1, 0, 19192, -231888] 2 196608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 58800.m have rank \(1\).

Modular form 58800.2.a.m

sage: E.q_eigenform(10)
\( q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.