# Properties

 Label 35280dy Number of curves $8$ Conductor $35280$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 35280dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bj7 35280dy1 [0, 0, 0, -289443, 21089698] [2] 442368 $$\Gamma_0(N)$$-optimal
35280.bj5 35280dy2 [0, 0, 0, -2547363, -1549971038] [2, 2] 884736
35280.bj4 35280dy3 [0, 0, 0, -18917283, 31669112482] [2] 1327104
35280.bj6 35280dy4 [0, 0, 0, -571683, -3892732382] [2] 1769472
35280.bj2 35280dy5 [0, 0, 0, -40649763, -99755096798] [2] 1769472
35280.bj3 35280dy6 [0, 0, 0, -19058403, 31172624098] [2, 2] 2654208
35280.bj8 35280dy7 [0, 0, 0, 5143677, 104935723522] [2] 5308416
35280.bj1 35280dy8 [0, 0, 0, -45518403, -74365731902] [2] 5308416

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.bj

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 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.