# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2112.b1")

sage: E.isogeny_class()

## Elliptic curves in class 2112.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.b1 2112t2 [0, -1, 0, -5169, -141327]  1920
2112.b2 2112t1 [0, -1, 0, -309, -2331]  960 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form2112.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - 2q^{7} + q^{9} - q^{11} - 6q^{13} + 2q^{15} - 4q^{17} - 2q^{19} + O(q^{20})$$

## 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. 