# Properties

 Label 2394.o Number of curves $2$ Conductor $2394$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2394.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.o1 2394i1 $$[1, -1, 1, -488, -3941]$$ $$651714363/14896$$ $$293197968$$ $$$$ $$1536$$ $$0.41122$$ $$\Gamma_0(N)$$-optimal
2394.o2 2394i2 $$[1, -1, 1, 52, -12581]$$ $$804357/3467044$$ $$-68241827052$$ $$$$ $$3072$$ $$0.75779$$

## Rank

sage: E.rank()

The elliptic curves in class 2394.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2394.o do not have complex multiplication.

## Modular form2394.2.a.o

sage: E.q_eigenform(10)

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

## 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. 