# Properties

 Label 320e Number of curves 2 Conductor 320 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("320.b1")

sage: E.isogeny_class()

## Elliptic curves in class 320e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320.b2 320e1 [0, 1, 0, 0, -2] [2] 16 $$\Gamma_0(N)$$-optimal
320.b1 320e2 [0, 1, 0, -25, -57] [2] 32

## Rank

sage: E.rank()

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

## Modular form320.2.a.b

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.