# Properties

 Label 58800ix Number of curves $6$ Conductor $58800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.jt1")

sage: E.isogeny_class()

## Elliptic curves in class 58800ix

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.jt5 58800ix1 [0, 1, 0, -78808, 18778388] [2] 589824 $$\Gamma_0(N)$$-optimal
58800.jt4 58800ix2 [0, 1, 0, -1646808, 812186388] [2, 2] 1179648
58800.jt3 58800ix3 [0, 1, 0, -2038808, 395882388] [2, 2] 2359296
58800.jt1 58800ix4 [0, 1, 0, -26342808, 52031690388] [2] 2359296
58800.jt6 58800ix5 [0, 1, 0, 7565192, 3065794388] [2] 4718592
58800.jt2 58800ix6 [0, 1, 0, -17914808, -28911213612] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 58800ix have rank $$0$$.

## Modular form 58800.2.a.jt

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.