# Properties

 Label 87360fu Number of curves 8 Conductor 87360 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("87360.eb1")

sage: E.isogeny_class()

## Elliptic curves in class 87360fu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
87360.eb7 87360fu1 [0, 1, 0, -1646401, -809304385] [2] 1769472 $$\Gamma_0(N)$$-optimal
87360.eb6 87360fu2 [0, 1, 0, -2649921, 292761279] [2, 2] 3538944
87360.eb5 87360fu3 [0, 1, 0, -10171201, 11938220735] [2] 5308416
87360.eb8 87360fu4 [0, 1, 0, 10413759, 2333308095] [2] 7077888
87360.eb4 87360fu5 [0, 1, 0, -31769921, 68800473279] [2] 7077888
87360.eb2 87360fu6 [0, 1, 0, -160761921, 784498732479] [2, 2] 10616832
87360.eb3 87360fu7 [0, 1, 0, -158786241, 804722188095] [2] 21233664
87360.eb1 87360fu8 [0, 1, 0, -2572189121, 50210557479999] [2] 21233664

## Rank

sage: E.rank()

The elliptic curves in class 87360fu have rank $$1$$.

## Modular form 87360.2.a.eb

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - q^{13} - q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.