# Properties

 Label 58800gb Number of curves 6 Conductor 58800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.m1")
sage: E.isogeny_class()

## Elliptic curves in class 58800gb

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

## Rank

sage: E.rank()

The elliptic curves in class 58800gb 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 