# Properties

 Label 88935bq Number of curves $6$ Conductor $88935$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("88935.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 88935bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.bv4 88935bq1 [1, 0, 1, -1571309, 757989131] [2] 1474560 $$\Gamma_0(N)$$-optimal
88935.bv3 88935bq2 [1, 0, 1, -1600954, 727893527] [2, 2] 2949120
88935.bv5 88935bq3 [1, 0, 1, 1511771, 3216828437] [2] 5898240
88935.bv2 88935bq4 [1, 0, 1, -5187999, -3687041459] [2, 2] 5898240
88935.bv6 88935bq5 [1, 0, 1, 10790656, -21915491083] [2] 11796480
88935.bv1 88935bq6 [1, 0, 1, -78559374, -268000082759] [2] 11796480

## Rank

sage: E.rank()

The elliptic curves in class 88935bq have rank $$0$$.

## Modular form 88935.2.a.bv

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.