# Properties

 Label 320790.ci Number of curves $6$ Conductor $320790$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("320790.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 320790.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
320790.ci1 320790ci3 [1, 0, 0, -98550451, 376553391905] [2] 35389440
320790.ci2 320790ci6 [1, 0, 0, -87603131, -314228388759] [2] 70778880
320790.ci3 320790ci4 [1, 0, 0, -8474931, 1065836961] [2, 2] 35389440
320790.ci4 320790ci2 [1, 0, 0, -6162931, 5876184161] [2, 2] 17694720
320790.ci5 320790ci1 [1, 0, 0, -244211, 159884385] [2] 8847360 $$\Gamma_0(N)$$-optimal
320790.ci6 320790ci5 [1, 0, 0, 33661269, 8507089881] [2] 70778880

## Rank

sage: E.rank()

The elliptic curves in class 320790.ci have rank $$1$$.

## Modular form 320790.2.a.ci

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.