# Properties

 Label 212160.b Number of curves 4 Conductor 212160 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("212160.b1")

sage: E.isogeny_class()

## Elliptic curves in class 212160.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.b1 212160de4 [0, -1, 0, -4903681, -4170818399] [2] 8847360
212160.b2 212160de3 [0, -1, 0, -4110081, 3191910561] [2] 8847360
212160.b3 212160de2 [0, -1, 0, -410881, -16775519] [2, 2] 4423680
212160.b4 212160de1 [0, -1, 0, 101119, -2132319] [2] 2211840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 212160.b have rank $$0$$.

## Modular form 212160.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 4q^{7} + q^{9} - 4q^{11} - q^{13} + q^{15} - q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.