# Properties

 Label 320c Number of curves 4 Conductor 320 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("320.f1")

sage: E.isogeny_class()

## Elliptic curves in class 320c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.f3 320c1 [0, -1, 0, -5, 5]  16 $$\Gamma_0(N)$$-optimal
320.f4 320c2 [0, -1, 0, 15, 17]  32
320.f1 320c3 [0, -1, 0, -165, -763]  48
320.f2 320c4 [0, -1, 0, -145, -975]  96

## Rank

sage: E.rank()

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

## Modular form320.2.a.f

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 Cremona 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 Cremona labels. 