# Properties

 Label 2112.l Number of curves 4 Conductor 2112 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2112.l1")

sage: E.isogeny_class()

## Elliptic curves in class 2112.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.l1 2112f3 [0, -1, 0, -577, -4607] [2] 1024
2112.l2 2112f2 [0, -1, 0, -137, 585] [2, 2] 512
2112.l3 2112f1 [0, -1, 0, -132, 630] [2] 256 $$\Gamma_0(N)$$-optimal
2112.l4 2112f4 [0, -1, 0, 223, 2817] [4] 1024

## Rank

sage: E.rank()

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

## Modular form2112.2.a.l

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.