# Properties

 Label 7350.cs Number of curves 8 Conductor 7350 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.cs1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.cs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.cs1 7350ck7 [1, 0, 0, -430259838, 3435103244292] [2] 1327104
7350.cs2 7350ck6 [1, 0, 0, -26891838, 53669300292] [2, 2] 663552
7350.cs3 7350ck8 [1, 0, 0, -24931838, 61824860292] [2] 1327104
7350.cs4 7350ck4 [1, 0, 0, -5337963, 4663009917] [2] 442368
7350.cs5 7350ck3 [1, 0, 0, -1803838, 708532292] [2] 331776
7350.cs6 7350ck2 [1, 0, 0, -707463, -120296583] [2, 2] 221184
7350.cs7 7350ck1 [1, 0, 0, -609463, -183114583] [2] 110592 $$\Gamma_0(N)$$-optimal
7350.cs8 7350ck5 [1, 0, 0, 2355037, -882859083] [2] 442368

## Rank

sage: E.rank()

The elliptic curves in class 7350.cs have rank $$0$$.

## Modular form7350.2.a.cs

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 2q^{13} + q^{16} - 6q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.