# Properties

 Label 4998.bq Number of curves $6$ Conductor $4998$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4998.bq1")

sage: E.isogeny_class()

## Elliptic curves in class 4998.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4998.bq1 4998bm5 [1, 0, 0, -672211597, 6708160798793] [2] 1474560
4998.bq2 4998bm3 [1, 0, 0, -42093157, 104393523905] [2, 2] 737280
4998.bq3 4998bm6 [1, 0, 0, -14337597, 240012741177] [2] 1474560
4998.bq4 4998bm2 [1, 0, 0, -4445477, -907037055] [2, 2] 368640
4998.bq5 4998bm1 [1, 0, 0, -3441957, -2455067007] [2] 184320 $$\Gamma_0(N)$$-optimal
4998.bq6 4998bm4 [1, 0, 0, 17145883, -7129667007] [2] 737280

## Rank

sage: E.rank()

The elliptic curves in class 4998.bq have rank $$0$$.

## Modular form4998.2.a.bq

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} + 2q^{13} + 2q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.