# Properties

 Label 320.b Number of curves $2$ Conductor $320$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 320.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320.b1 320e2 $$[0, 1, 0, -25, -57]$$ $$438976/5$$ $$20480$$ $$$$ $$32$$ $$-0.35947$$
320.b2 320e1 $$[0, 1, 0, 0, -2]$$ $$-64/25$$ $$-1600$$ $$$$ $$16$$ $$-0.70605$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 320.b do not have complex multiplication.

## Modular form320.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 