# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("35280.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 35280el

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.cv4 35280el1 [0, 0, 0, 16317, 1278018]  147456 $$\Gamma_0(N)$$-optimal
35280.cv3 35280el2 [0, 0, 0, -124803, 13724802] [2, 2] 294912
35280.cv2 35280el3 [0, 0, 0, -618723, -175051422]  589824
35280.cv1 35280el4 [0, 0, 0, -1888803, 999095202]  589824

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.cv

sage: E.q_eigenform(10)

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

## 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. 