# Properties

 Label 303450ey Number of curves $2$ Conductor $303450$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ey1")

sage: E.isogeny_class()

## Elliptic curves in class 303450ey

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.ey2 303450ey1 $$[1, 1, 1, 588687, 207806031]$$ $$59822347031/83966400$$ $$-31667887088775000000$$ $$$$ $$7962624$$ $$2.4274$$ $$\Gamma_0(N)$$-optimal
303450.ey1 303450ey2 $$[1, 1, 1, -3746313, 2054516031]$$ $$15417797707369/4080067320$$ $$1538795413455391875000$$ $$$$ $$15925248$$ $$2.7740$$

## Rank

sage: E.rank()

The elliptic curves in class 303450ey have rank $$1$$.

## Complex multiplication

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

## Modular form 303450.2.a.ey

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - 2q^{11} - q^{12} + 2q^{13} + q^{14} + q^{16} + q^{18} - 4q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 