# Properties

 Label 166464.fz Number of curves 6 Conductor 166464 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("166464.fz1")

sage: E.isogeny_class()

## Elliptic curves in class 166464.fz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166464.fz1 166464gb5 [0, 0, 0, -4618380684, 120804386941168]  56623104
166464.fz2 166464gb3 [0, 0, 0, -288652044, 1887523897840] [2, 2] 28311552
166464.fz3 166464gb6 [0, 0, 0, -273670284, 2092192717552]  56623104
166464.fz4 166464gb2 [0, 0, 0, -18980364, 26249962480] [2, 2] 14155776
166464.fz5 166464gb1 [0, 0, 0, -5663244, -4810888208]  7077888 $$\Gamma_0(N)$$-optimal
166464.fz6 166464gb4 [0, 0, 0, 37617396, 152870471152]  28311552

## Rank

sage: E.rank()

The elliptic curves in class 166464.fz have rank $$0$$.

## Modular form 166464.2.a.fz

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 