# Properties

 Label 70602.bf Number of curves $6$ Conductor $70602$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("70602.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 70602.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
70602.bf1 70602bn4 [1, 0, 0, -2259299, 1306911333] [2] 1105920
70602.bf2 70602bn6 [1, 0, 0, -1536469, -726140497] [2] 2211840
70602.bf3 70602bn3 [1, 0, 0, -174859, 9945869] [2, 2] 1105920
70602.bf4 70602bn2 [1, 0, 0, -141239, 20401689] [2, 2] 552960
70602.bf5 70602bn1 [1, 0, 0, -6759, 471753] [2] 276480 $$\Gamma_0(N)$$-optimal
70602.bf6 70602bn5 [1, 0, 0, 648831, 76994235] [2] 2211840

## Rank

sage: E.rank()

The elliptic curves in class 70602.bf have rank $$0$$.

## Modular form 70602.2.a.bf

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} - 6q^{13} + q^{14} - 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.