# Properties

 Label 320.a Number of curves 4 Conductor 320 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("320.a1")

sage: E.isogeny_class()

## Elliptic curves in class 320.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.a1 320f3 [0, 1, 0, -165, 763]  48
320.a2 320f4 [0, 1, 0, -145, 975]  96
320.a3 320f1 [0, 1, 0, -5, -5]  16 $$\Gamma_0(N)$$-optimal
320.a4 320f2 [0, 1, 0, 15, -17]  32

## Rank

sage: E.rank()

The elliptic curves in class 320.a have rank $$1$$.

## Modular form320.2.a.a

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 