# Properties

 Label 212160gc Number of curves 4 Conductor 212160 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("212160.ft1")

sage: E.isogeny_class()

## Elliptic curves in class 212160gc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.ft4 212160gc1 [0, 1, 0, 101119, 2132319]  2211840 $$\Gamma_0(N)$$-optimal
212160.ft3 212160gc2 [0, 1, 0, -410881, 16775519] [2, 2] 4423680
212160.ft1 212160gc3 [0, 1, 0, -4903681, 4170818399]  8847360
212160.ft2 212160gc4 [0, 1, 0, -4110081, -3191910561]  8847360

## Rank

sage: E.rank()

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

## Modular form 212160.2.a.ft

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 Cremona 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 Cremona labels. 