# Properties

 Label 2112.o Number of curves 2 Conductor 2112 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2112.o1")

sage: E.isogeny_class()

## Elliptic curves in class 2112.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.o1 2112i1 [0, -1, 0, -41, -87]  384 $$\Gamma_0(N)$$-optimal
2112.o2 2112i2 [0, -1, 0, -1, -287]  768

## Rank

sage: E.rank()

The elliptic curves in class 2112.o have rank $$0$$.

## Modular form2112.2.a.o

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{5} - 2q^{7} + q^{9} + q^{11} - 4q^{13} - 4q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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. 