# Properties

 Label 129360fo Number of curves 4 Conductor 129360 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("129360.dh1")

sage: E.isogeny_class()

## Elliptic curves in class 129360fo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
129360.dh3 129360fo1 [0, -1, 0, -392800, -82146560] [2] 1769472 $$\Gamma_0(N)$$-optimal
129360.dh2 129360fo2 [0, -1, 0, -1662880, 743913472] [2, 2] 3538944
129360.dh4 129360fo3 [0, -1, 0, 2217920, 3696426112] [2] 7077888
129360.dh1 129360fo4 [0, -1, 0, -25864960, 50638921600] [4] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 129360fo have rank $$1$$.

## Modular form 129360.2.a.dh

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + q^{11} - 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.