# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.dn1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.dn1 35280fs8 [0, 0, 0, -13553164947, 607308275951314] [2] 18874368
35280.dn2 35280fs6 [0, 0, 0, -847072947, 9489188569714] [2, 2] 9437184
35280.dn3 35280fs7 [0, 0, 0, -841780947, 9613604548114] [2] 18874368
35280.dn4 35280fs4 [0, 0, 0, -106334067, -421926912974] [2] 4718592
35280.dn5 35280fs3 [0, 0, 0, -53272947, 146321329714] [2, 2] 4718592
35280.dn6 35280fs2 [0, 0, 0, -7550067, -4683053774] [2, 2] 2359296
35280.dn7 35280fs1 [0, 0, 0, 1481613, -523061966] [2] 1179648 $$\Gamma_0(N)$$-optimal
35280.dn8 35280fs5 [0, 0, 0, 8960973, 467734632946] [2] 9437184

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.dn

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.