# Properties

 Label 9016.e Number of curves $2$ Conductor $9016$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9016.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9016.e1 9016i2 $$[0, 1, 0, -23928, -1432544]$$ $$12576878500/1127$$ $$135772593152$$ $$$$ $$15360$$ $$1.1762$$
9016.e2 9016i1 $$[0, 1, 0, -1388, -26048]$$ $$-9826000/3703$$ $$-111527487232$$ $$$$ $$7680$$ $$0.82963$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9016.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9016.e do not have complex multiplication.

## Modular form9016.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})$$ ## 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. 