# Properties

 Label 2535.j Number of curves 8 Conductor 2535 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2535.j1")

sage: E.isogeny_class()

## Elliptic curves in class 2535.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2535.j1 2535a7 [1, 1, 0, -365043, -85043772] [2] 9216
2535.j2 2535a5 [1, 1, 0, -22818, -1335537] [2, 2] 4608
2535.j3 2535a8 [1, 1, 0, -18593, -1840002] [2] 9216
2535.j4 2535a4 [1, 1, 0, -13523, 599682] [2] 2304
2535.j5 2535a3 [1, 1, 0, -1693, -13112] [2, 2] 2304
2535.j6 2535a2 [1, 1, 0, -848, 9027] [2, 2] 1152
2535.j7 2535a1 [1, 1, 0, -3, 408] [2] 576 $$\Gamma_0(N)$$-optimal
2535.j8 2535a6 [1, 1, 0, 5912, -90683] [2] 4608

## Rank

sage: E.rank()

The elliptic curves in class 2535.j have rank $$1$$.

## Modular form2535.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} + q^{15} - q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.