# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("35280.el1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.el

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.el1 35280dg3 [0, 0, 0, -329427, -63771246]  331776
35280.el2 35280dg1 [0, 0, 0, -82467, 9103906]  110592 $$\Gamma_0(N)$$-optimal
35280.el3 35280dg2 [0, 0, 0, -58947, 14405314]  221184
35280.el4 35280dg4 [0, 0, 0, 517293, -337600494]  663552

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.el

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 