# Properties

 Label 35280.fr Number of curves 4 Conductor 35280 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.fr1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.fr1 35280ck4 [0, 0, 0, -47187, 3945186] [2] 73728
35280.fr2 35280ck2 [0, 0, 0, -3087, 55566] [2, 2] 36864
35280.fr3 35280ck1 [0, 0, 0, -882, -9261] [2] 18432 $$\Gamma_0(N)$$-optimal
35280.fr4 35280ck3 [0, 0, 0, 5733, 314874] [2] 73728

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.fr

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.