# Properties

 Label 320d Number of curves 2 Conductor 320 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("320.e1")

sage: E.isogeny_class()

## Elliptic curves in class 320d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.e2 320d1 [0, -1, 0, 0, 2]  16 $$\Gamma_0(N)$$-optimal
320.e1 320d2 [0, -1, 0, -25, 57]  32

## Rank

sage: E.rank()

The elliptic curves in class 320d have rank $$0$$.

## Modular form320.2.a.e

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 2q^{7} + q^{9} + 4q^{11} + 6q^{13} + 2q^{15} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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. 