# Properties

 Label 83790ck Number of curves $4$ Conductor $83790$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("83790.cl1")

sage: E.isogeny_class()

## Elliptic curves in class 83790ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
83790.cl4 83790ck1 [1, -1, 0, -4419, 194053]  221184 $$\Gamma_0(N)$$-optimal
83790.cl3 83790ck2 [1, -1, 0, -83799, 9354505] [2, 2] 442368
83790.cl2 83790ck3 [1, -1, 0, -97029, 6213703]  884736
83790.cl1 83790ck4 [1, -1, 0, -1340649, 597811675]  884736

## Rank

sage: E.rank()

The elliptic curves in class 83790ck have rank $$1$$.

## Modular form 83790.2.a.cl

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + q^{19} + O(q^{20})$$

## 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 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. 