# Properties

 Label 303450.eo Number of curves $4$ Conductor $303450$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eo1")

sage: E.isogeny_class()

## Elliptic curves in class 303450.eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.eo1 303450eo3 [1, 1, 1, -2698688, 1705259531]  7077888
303450.eo2 303450eo2 [1, 1, 1, -169938, 26169531] [2, 2] 3538944
303450.eo3 303450eo1 [1, 1, 1, -25438, -996469]  1769472 $$\Gamma_0(N)$$-optimal
303450.eo4 303450eo4 [1, 1, 1, 46812, 88593531]  7077888

## Rank

sage: E.rank()

The elliptic curves in class 303450.eo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 303450.eo do not have complex multiplication.

## Modular form 303450.2.a.eo

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{16} + q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 