# Properties

 Label 493680.go Number of curves 6 Conductor 493680 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("493680.go1")

sage: E.isogeny_class()

## Elliptic curves in class 493680.go

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
493680.go1 493680go6 [0, 1, 0, -565583080, -5176745911372] [u'2'] 141557760
493680.go2 493680go4 [0, 1, 0, -38507080, -65584524172] [u'2', u'2'] 70778880
493680.go3 493680go2 [0, 1, 0, -14307080, 20015715828] [u'2', u'2'] 35389440
493680.go4 493680go1 [0, 1, 0, -14152200, 20487232500] [u'2'] 17694720 $$\Gamma_0(N)$$-optimal
493680.go5 493680go3 [0, 1, 0, 7414840, 75441366900] [u'2'] 70778880
493680.go6 493680go5 [0, 1, 0, 101368920, -432451296972] [u'2'] 141557760

## Rank

sage: E.rank()

The elliptic curves in class 493680.go have rank $$1$$.

## Modular form 493680.2.a.go

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.