# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 322c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322.d2 322c1 $$[1, 1, 1, -4, 1]$$ $$7189057/644$$ $$644$$ $$$$ $$24$$ $$-0.72126$$ $$\Gamma_0(N)$$-optimal
322.d1 322c2 $$[1, 1, 1, -14, -23]$$ $$304821217/51842$$ $$51842$$ $$$$ $$48$$ $$-0.37469$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form322.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} - 2q^{5} + 2q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} + 6q^{11} + 2q^{12} - 4q^{13} + q^{14} - 4q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 