# Properties

 Label 322b Number of curves $2$ Conductor $322$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 322b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322.b2 322b1 $$[1, 1, 0, 35, 381]$$ $$4533086375/60669952$$ $$-60669952$$ $$$$ $$112$$ $$0.17418$$ $$\Gamma_0(N)$$-optimal
322.b1 322b2 $$[1, 1, 0, -605, 5117]$$ $$24553362849625/1755162752$$ $$1755162752$$ $$$$ $$224$$ $$0.52075$$

## Rank

sage: E.rank()

The elliptic curves in class 322b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 322b do not have complex multiplication.

## Modular form322.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} + q^{7} - q^{8} + q^{9} + 4q^{11} + 2q^{12} - q^{14} + q^{16} + 6q^{17} - q^{18} - 6q^{19} + O(q^{20})$$ ## 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. 