# Properties

 Label 35280ff Number of curves 4 Conductor 35280 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.es1")

sage: E.isogeny_class()

## Elliptic curves in class 35280ff

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.es3 35280ff1 [0, 0, 0, -17787, -865046] [2] 98304 $$\Gamma_0(N)$$-optimal
35280.es2 35280ff2 [0, 0, 0, -53067, 3629626] [2, 2] 196608
35280.es4 35280ff3 [0, 0, 0, 123333, 22645546] [2] 393216
35280.es1 35280ff4 [0, 0, 0, -793947, 272272714] [4] 393216

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.es

sage: E.q_eigenform(10)

$$q + q^{5} + 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.