# Properties

 Label 3380i Number of curves 4 Conductor 3380 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3380.c1")

sage: E.isogeny_class()

## Elliptic curves in class 3380i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3380.c3 3380i1 [0, 1, 0, -225, 820]  1152 $$\Gamma_0(N)$$-optimal
3380.c4 3380i2 [0, 1, 0, 620, 6228]  2304
3380.c1 3380i3 [0, 1, 0, -6985, -226992]  3456
3380.c2 3380i4 [0, 1, 0, -6140, -283100]  6912

## Rank

sage: E.rank()

The elliptic curves in class 3380i have rank $$1$$.

## Modular form3380.2.a.c

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 