# Properties

 Label 35280em Number of curves $4$ Conductor $35280$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("em1")

sage: E.isogeny_class()

## Elliptic curves in class 35280em

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.p3 35280em1 [0, 0, 0, -24843, 951482] [2] 147456 $$\Gamma_0(N)$$-optimal
35280.p2 35280em2 [0, 0, 0, -165963, -25325062] [2, 2] 294912
35280.p4 35280em3 [0, 0, 0, 45717, -85484518] [2] 589824
35280.p1 35280em4 [0, 0, 0, -2635563, -1646864422] [2] 589824

## Rank

sage: E.rank()

The elliptic curves in class 35280em have rank $$2$$.

## Complex multiplication

The elliptic curves in class 35280em do not have complex multiplication.

## Modular form 35280.2.a.em

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} + 2q^{13} - 6q^{17} + O(q^{20})$$

## 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.