# Properties

 Label 185020.o Number of curves $4$ Conductor $185020$ CM no Rank $2$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 185020.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185020.o1 185020m4 [0, -1, 0, -5971380, -5614436728]  5225472
185020.o2 185020m3 [0, -1, 0, -374525, -86982730]  2612736
185020.o3 185020m2 [0, -1, 0, -84380, -5303128]  1741824
185020.o4 185020m1 [0, -1, 0, -38125, 2819250]  870912 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 185020.o have rank $$2$$.

## Complex multiplication

The elliptic curves in class 185020.o do not have complex multiplication.

## Modular form 185020.2.a.o

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 