# Properties

 Label 346560.je Number of curves $2$ Conductor $346560$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("je1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.je

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.je1 346560je2 $$[0, 1, 0, -84237665, -297610425825]$$ $$781484460931/900$$ $$76131579461920358400$$ $$[2]$$ $$28016640$$ $$3.0989$$
346560.je2 346560je1 $$[0, 1, 0, -5221985, -4730906337]$$ $$-186169411/6480$$ $$-548147372125826580480$$ $$[2]$$ $$14008320$$ $$2.7524$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.je have rank $$0$$.

## Complex multiplication

The elliptic curves in class 346560.je do not have complex multiplication.

## Modular form 346560.2.a.je

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2 q^{7} + q^{9} - 2 q^{13} + q^{15} - 6 q^{17} + O(q^{20})$$

## 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.