# Properties

 Label 847a Number of curves $3$ Conductor $847$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 847a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
847.c1 847a1 $$[0, 1, 1, -10809, -436166]$$ $$-78843215872/539$$ $$-954871379$$ $$[]$$ $$800$$ $$0.90395$$ $$\Gamma_0(N)$$-optimal
847.c2 847a2 $$[0, 1, 1, -5969, -822761]$$ $$-13278380032/156590819$$ $$-277410187898459$$ $$[]$$ $$2400$$ $$1.4533$$
847.c3 847a3 $$[0, 1, 1, 53321, 21262764]$$ $$9463555063808/115539436859$$ $$-204685160301366899$$ $$[]$$ $$7200$$ $$2.0026$$

## Rank

sage: E.rank()

The elliptic curves in class 847a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 847a do not have complex multiplication.

## Modular form847.2.a.a

sage: E.q_eigenform(10)

$$q + q^{3} - 2 q^{4} + 3 q^{5} - q^{7} - 2 q^{9} - 2 q^{12} + 4 q^{13} + 3 q^{15} + 4 q^{16} + 6 q^{17} - 2 q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 