# Properties

 Label 66240.ez Number of curves $6$ Conductor $66240$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("66240.ez1")

sage: E.isogeny_class()

## Elliptic curves in class 66240.ez

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
66240.ez1 66240cw4 [0, 0, 0, -63590412, -195180115984] [2] 2359296
66240.ez2 66240cw6 [0, 0, 0, -14878092, 18920874224] [4] 4718592
66240.ez3 66240cw3 [0, 0, 0, -4078092, -2882165776] [2, 2] 2359296
66240.ez4 66240cw2 [0, 0, 0, -3974412, -3049671184] [2, 2] 1179648
66240.ez5 66240cw1 [0, 0, 0, -241932, -50250256] [2] 589824 $$\Gamma_0(N)$$-optimal
66240.ez6 66240cw5 [0, 0, 0, 5063028, -13964859664] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 66240.ez have rank $$0$$.

## Modular form 66240.2.a.ez

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.