# Properties

 Label 152880ee Number of curves $6$ Conductor $152880$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("152880.i1")

sage: E.isogeny_class()

## Elliptic curves in class 152880ee

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152880.i6 152880ee1 [0, -1, 0, 11744, 192256] [2] 589824 $$\Gamma_0(N)$$-optimal
152880.i5 152880ee2 [0, -1, 0, -50976, 1647360] [2, 2] 1179648
152880.i2 152880ee3 [0, -1, 0, -662496, 207607296] [2] 2359296
152880.i3 152880ee4 [0, -1, 0, -442976, -112189440] [2, 2] 2359296
152880.i4 152880ee5 [0, -1, 0, -90176, -286331520] [2] 4718592
152880.i1 152880ee6 [0, -1, 0, -7067776, -7229874560] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 152880ee have rank $$1$$.

## Modular form 152880.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 4q^{11} - q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.