# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.ct1")

sage: E.isogeny_class()

## Elliptic curves in class 7350cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.ct8 7350cj1 [1, 0, 0, 1812, -91008] [2] 13824 $$\Gamma_0(N)$$-optimal
7350.ct6 7350cj2 [1, 0, 0, -22688, -1193508] [2, 2] 27648
7350.ct7 7350cj3 [1, 0, 0, -16563, 2683617] [2] 41472
7350.ct4 7350cj4 [1, 0, 0, -353438, -80904258] [2] 55296
7350.ct5 7350cj5 [1, 0, 0, -83938, 8055242] [2] 55296
7350.ct3 7350cj6 [1, 0, 0, -408563, 100291617] [2, 2] 82944
7350.ct2 7350cj7 [1, 0, 0, -555563, 21646617] [2] 165888
7350.ct1 7350cj8 [1, 0, 0, -6533563, 6427416617] [2] 165888

## Rank

sage: E.rank()

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

## Modular form7350.2.a.ct

sage: E.q_eigenform(10)

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

## 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.