# Properties

 Label 286650.ji Number of curves $2$ Conductor $286650$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ji1")

sage: E.isogeny_class()

## Elliptic curves in class 286650.ji

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.ji1 286650ji2 $$[1, -1, 1, -507380, -124488003]$$ $$10779215329/1232010$$ $$1651011230206406250$$ $$[2]$$ $$6635520$$ $$2.2279$$
286650.ji2 286650ji1 $$[1, -1, 1, 43870, -9828003]$$ $$6967871/35100$$ $$-47037356985937500$$ $$[2]$$ $$3317760$$ $$1.8814$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 286650.ji do not have complex multiplication.

## Modular form 286650.2.a.ji

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.