# Properties

 Label 327600.ks Number of curves 8 Conductor 327600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("327600.ks1")

sage: E.isogeny_class()

## Elliptic curves in class 327600.ks

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
327600.ks1 327600ks8 [0, 0, 0, -144685638075, -21182940650969750] [2] 509607936
327600.ks2 327600ks6 [0, 0, 0, -9042858075, -330983009909750] [2, 2] 254803968
327600.ks3 327600ks7 [0, 0, 0, -8931726075, -339514502417750] [2] 509607936
327600.ks4 327600ks5 [0, 0, 0, -1787058075, -29029667309750] [2] 169869312
327600.ks5 327600ks3 [0, 0, 0, -572130075, -5037867197750] [2] 127401984
327600.ks6 327600ks2 [0, 0, 0, -149058075, -123881309750] [2, 2] 84934656
327600.ks7 327600ks1 [0, 0, 0, -92610075, 341193762250] [2] 42467328 $$\Gamma_0(N)$$-optimal
327600.ks8 327600ks4 [0, 0, 0, 585773925, -982899917750] [2] 169869312

## Rank

sage: E.rank()

The elliptic curves in class 327600.ks have rank $$0$$.

## Modular form 327600.2.a.ks

sage: E.q_eigenform(10)

$$q + q^{7} - q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.