# Properties

 Label 360e Number of curves 4 Conductor 360 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("360.a1")

sage: E.isogeny_class()

## Elliptic curves in class 360e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
360.a3 360e1 [0, 0, 0, -18, -27]  32 $$\Gamma_0(N)$$-optimal
360.a2 360e2 [0, 0, 0, -63, 162] [2, 2] 64
360.a1 360e3 [0, 0, 0, -963, 11502]  128
360.a4 360e4 [0, 0, 0, 117, 918]  128

## Rank

sage: E.rank()

The elliptic curves in class 360e have rank $$1$$.

## Modular form360.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 