# Properties

 Label 366597.o Number of curves 6 Conductor 366597 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("366597.o1")

sage: E.isogeny_class()

## Elliptic curves in class 366597.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
366597.o1 366597o6 [1, -1, 0, -21515058, -38406159239] [2] 16220160
366597.o2 366597o4 [1, -1, 0, -1352223, -592778480] [2, 2] 8110080
366597.o3 366597o2 [1, -1, 0, -185778, 17272255] [2, 2] 4055040
366597.o4 366597o1 [1, -1, 0, -161973, 25123144] [2] 2027520 $$\Gamma_0(N)$$-optimal
366597.o5 366597o5 [1, -1, 0, 147492, -1836642101] [2] 16220160
366597.o6 366597o3 [1, -1, 0, 599787, 124580434] [2] 8110080

## Rank

sage: E.rank()

The elliptic curves in class 366597.o have rank $$1$$.

## Modular form 366597.2.a.o

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 2q^{10} - q^{11} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.