# Properties

 Label 156702bg Number of curves 2 Conductor 156702 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("156702.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 156702bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156702.bu1 156702bg1 [1, 1, 1, -7634495, -8124541531] [] 6322176 $$\Gamma_0(N)$$-optimal
156702.bu2 156702bg2 [1, 1, 1, 42364615, 358508096729] [] 44255232

## Rank

sage: E.rank()

The elliptic curves in class 156702bg have rank $$1$$.

## Modular form 156702.2.a.bu

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.