# Properties

 Label 9576.e Number of curves $4$ Conductor $9576$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 9576.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9576.e1 9576g3 $$[0, 0, 0, -29091, 1584830]$$ $$1823652903746/328593657$$ $$490587701151744$$ $$$$ $$40960$$ $$1.5379$$
9576.e2 9576g2 $$[0, 0, 0, -8571, -282490]$$ $$93280467172/7800849$$ $$5823302575104$$ $$[2, 2]$$ $$20480$$ $$1.1913$$
9576.e3 9576g1 $$[0, 0, 0, -8391, -295846]$$ $$350104249168/2793$$ $$521240832$$ $$$$ $$10240$$ $$0.84476$$ $$\Gamma_0(N)$$-optimal
9576.e4 9576g4 $$[0, 0, 0, 9069, -1295026]$$ $$55251546334/517244049$$ $$-772241227204608$$ $$$$ $$40960$$ $$1.5379$$

## Rank

sage: E.rank()

The elliptic curves in class 9576.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9576.e do not have complex multiplication.

## Modular form9576.2.a.e

sage: E.q_eigenform(10)

$$q - 2 q^{5} - q^{7} + 4 q^{11} - 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 