# Properties

 Label 338130y Number of curves 8 Conductor 338130 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("338130.y1")

sage: E.isogeny_class()

## Elliptic curves in class 338130y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.y7 338130y1 [1, -1, 0, -5452075800, -149202592145600] [2] 637009920 $$\Gamma_0(N)$$-optimal
338130.y6 338130y2 [1, -1, 0, -14454448920, 470482963468096] [2, 2] 1274019840
338130.y5 338130y3 [1, -1, 0, -67087036440, 6644606911560256] [2] 1911029760
338130.y4 338130y4 [1, -1, 0, -211651864920, 37473670967754496] [2] 2548039680
338130.y8 338130y5 [1, -1, 0, 38704997160, 3127062489980800] [2] 2548039680
338130.y2 338130y6 [1, -1, 0, -1071449453160, 426880086563858800] [2, 2] 3822059520
338130.y1 338130y7 [1, -1, 0, -17143191015660, 27320313468836296300L] [2] 7644119040
338130.y3 338130y8 [1, -1, 0, -1069506558180, 428505349689527476] [2] 7644119040

## Rank

sage: E.rank()

The elliptic curves in class 338130y have rank $$1$$.

## Modular form 338130.2.a.y

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + 4q^{7} - q^{8} + q^{10} + q^{13} - 4q^{14} + q^{16} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.