# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("320.c1")

sage: E.isogeny_class()

## Elliptic curves in class 320b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.c3 320b1 [0, 0, 0, -8, 8]  16 $$\Gamma_0(N)$$-optimal
320.c2 320b2 [0, 0, 0, -28, -48] [2, 2] 32
320.c1 320b3 [0, 0, 0, -428, -3408]  64
320.c4 320b4 [0, 0, 0, 52, -272]  64

## Rank

sage: E.rank()

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

## Modular form320.2.a.c

sage: E.q_eigenform(10)

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

## 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. 