# Properties

 Label 35280.ek Number of curves 8 Conductor 35280 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.ek1 35280fe8 [0, 0, 0, -2478296667, 47487362908426] [4] 10616832
35280.ek2 35280fe6 [0, 0, 0, -154896987, 741955386634] [2, 2] 5308416
35280.ek3 35280fe7 [0, 0, 0, -143607387, 854695590154] [2] 10616832
35280.ek4 35280fe5 [0, 0, 0, -30746667, 64467598426] [4] 3538944
35280.ek5 35280fe3 [0, 0, 0, -10390107, 9796828426] [2] 2654208
35280.ek6 35280fe2 [0, 0, 0, -4074987, -1662164966] [2, 2] 1769472
35280.ek7 35280fe1 [0, 0, 0, -3510507, -2530673894] [2] 884736 $$\Gamma_0(N)$$-optimal
35280.ek8 35280fe4 [0, 0, 0, 13565013, -12207356966] [2] 3538944

## Rank

sage: E.rank()

The elliptic curves in class 35280.ek have rank $$1$$.

## Modular form 35280.2.a.ek

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 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.