# Properties

 Label 35280.cg Number of curves $2$ Conductor $35280$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.cg1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.cg1 35280ed1 [0, 0, 0, -2163, -14798]  36864 $$\Gamma_0(N)$$-optimal
35280.cg2 35280ed2 [0, 0, 0, 7917, -113582]  73728

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.cg

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 