# Properties

 Label 8400.o Number of curves $2$ Conductor $8400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 8400.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.o1 8400bx2 $$[0, -1, 0, -1708, 24412]$$ $$1102736/147$$ $$73500000000$$ $$$$ $$7680$$ $$0.81273$$
8400.o2 8400bx1 $$[0, -1, 0, 167, 1912]$$ $$16384/63$$ $$-1968750000$$ $$$$ $$3840$$ $$0.46616$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8400.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8400.o do not have complex multiplication.

## Modular form8400.2.a.o

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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 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. 