# Properties

 Label 35280.bp Number of curves 8 Conductor 35280 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bp1 35280dx7 [0, 0, 0, -37633323, 88860133978] [2] 1327104
35280.bp2 35280dx8 [0, 0, 0, -3200043, 299882842] [2] 1327104
35280.bp3 35280dx6 [0, 0, 0, -2353323, 1386901978] [2, 2] 663552
35280.bp4 35280dx5 [0, 0, 0, -2035803, -1118013302] [2] 442368
35280.bp5 35280dx4 [0, 0, 0, -483483, 111452362] [2] 442368
35280.bp6 35280dx2 [0, 0, 0, -130683, -16472918] [2, 2] 221184
35280.bp7 35280dx3 [0, 0, 0, -95403, 37117402] [2] 331776
35280.bp8 35280dx1 [0, 0, 0, 10437, -1260182] [2] 110592 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 35280.bp have rank $$0$$.

## Modular form 35280.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.