# Properties

 Label 88935.j Number of curves 4 Conductor 88935 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("88935.j1")

sage: E.isogeny_class()

## Elliptic curves in class 88935.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.j1 88935p4 [1, 1, 1, -667136, -209997292]  1105920
88935.j2 88935p2 [1, 1, 1, -44591, -2814316] [2, 2] 552960
88935.j3 88935p1 [1, 1, 1, -14946, 660078]  276480 $$\Gamma_0(N)$$-optimal
88935.j4 88935p3 [1, 1, 1, 103634, -17399656]  1105920

## Rank

sage: E.rank()

The elliptic curves in class 88935.j have rank $$1$$.

## Modular form 88935.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3q^{8} + q^{9} + q^{10} + q^{12} - 6q^{13} + q^{15} - q^{16} + 2q^{17} - q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 