# Properties

 Label 361722u Number of curves 2 Conductor 361722 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("361722.u1")

sage: E.isogeny_class()

## Elliptic curves in class 361722u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
361722.u2 361722u1 [1, 1, 1, -1632, 104769]  995328 $$\Gamma_0(N)$$-optimal
361722.u1 361722u2 [1, 1, 1, -44952, 3639681]  1990656

## Rank

sage: E.rank()

The elliptic curves in class 361722u have rank $$1$$.

## Modular form 361722.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} - 4q^{14} - 2q^{15} + q^{16} - 4q^{17} + q^{18} + O(q^{20})$$

## 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 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. 