# Properties

 Label 35280dz Number of curves 4 Conductor 35280 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 35280dz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bk3 35280dz1 [0, 0, 0, -588, -3773]  17280 $$\Gamma_0(N)$$-optimal
35280.bk4 35280dz2 [0, 0, 0, 1617, -25382]  34560
35280.bk1 35280dz3 [0, 0, 0, -18228, 947023]  51840
35280.bk2 35280dz4 [0, 0, 0, -16023, 1184722]  103680

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.bk

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 