# Properties

 Label 212160.gy Number of curves $4$ Conductor $212160$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gy1")

sage: E.isogeny_class()

## Elliptic curves in class 212160.gy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.gy1 212160q3 $$[0, 1, 0, -130785, 18161055]$$ $$1887517194957938/21849165$$ $$2863813754880$$ $$$$ $$786432$$ $$1.5414$$
212160.gy2 212160q2 $$[0, 1, 0, -8385, 266175]$$ $$994958062276/98903025$$ $$6481708646400$$ $$[2, 2]$$ $$393216$$ $$1.1949$$
212160.gy3 212160q1 $$[0, 1, 0, -1905, -28017]$$ $$46689225424/7249905$$ $$118782443520$$ $$$$ $$196608$$ $$0.84829$$ $$\Gamma_0(N)$$-optimal
212160.gy4 212160q4 $$[0, 1, 0, 10335, 1303263]$$ $$931329171502/6107473125$$ $$-800518717440000$$ $$$$ $$786432$$ $$1.5414$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 212160.gy do not have complex multiplication.

## Modular form 212160.2.a.gy

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 