# Properties

 Label 9405.j Number of curves $2$ Conductor $9405$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 9405.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9405.j1 9405m2 $$[1, -1, 0, -279, -1620]$$ $$3301293169/218405$$ $$159217245$$ $$$$ $$3072$$ $$0.32326$$
9405.j2 9405m1 $$[1, -1, 0, -54, 135]$$ $$24137569/5225$$ $$3809025$$ $$$$ $$1536$$ $$-0.023311$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9405.j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9405.j do not have complex multiplication.

## Modular form9405.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + q^{11} + 6 q^{13} - 2 q^{14} - q^{16} - q^{19} + O(q^{20})$$

## 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. 