# Properties

 Label 337590di Number of curves $6$ Conductor $337590$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("337590.di1")

sage: E.isogeny_class()

## Elliptic curves in class 337590di

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
337590.di6 337590di1 [1, -1, 1, 65317, -36420469] [2] 5242880 $$\Gamma_0(N)$$-optimal
337590.di5 337590di2 [1, -1, 1, -1328603, -556631413] [2, 2] 10485760
337590.di4 337590di3 [1, -1, 1, -4029323, 2428204331] [2] 20971520
337590.di2 337590di4 [1, -1, 1, -20930603, -36851694613] [2, 2] 20971520
337590.di3 337590di5 [1, -1, 1, -20603903, -38058001693] [2] 41943040
337590.di1 337590di6 [1, -1, 1, -334889303, -2358764656333] [2] 41943040

## Rank

sage: E.rank()

The elliptic curves in class 337590di have rank $$0$$.

## Modular form 337590.2.a.di

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 6q^{13} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.