# Properties

 Label 286650l Number of curves 3 Conductor 286650 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("286650.l1")

sage: E.isogeny_class()

## Elliptic curves in class 286650l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.l3 286650l1 [1, -1, 0, 5283, 241191] [] 816480 $$\Gamma_0(N)$$-optimal
286650.l2 286650l2 [1, -1, 0, -49842, -8523684] [] 2449440
286650.l1 286650l3 [1, -1, 0, -5066217, -4387819059] [] 7348320

## Rank

sage: E.rank()

The elliptic curves in class 286650l have rank $$0$$.

## Modular form 286650.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 6q^{11} + q^{13} + q^{16} + 3q^{17} - 2q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.