# Properties

 Label 212160.gu Number of curves $2$ Conductor $212160$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gu1")

sage: E.isogeny_class()

## Elliptic curves in class 212160.gu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.gu1 212160p1 $$[0, 1, 0, -1124065, -458394337]$$ $$2396726313900986596/4154072495625$$ $$272241295073280000$$ $$$$ $$2949120$$ $$2.2393$$ $$\Gamma_0(N)$$-optimal
212160.gu2 212160p2 $$[0, 1, 0, -772545, -749945025]$$ $$-389032340685029858/1627263833203125$$ $$-213288725145600000000$$ $$$$ $$5898240$$ $$2.5859$$

## Rank

sage: E.rank()

The elliptic curves in class 212160.gu have rank $$1$$.

## Complex multiplication

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

## Modular form 212160.2.a.gu

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + 2 q^{11} + q^{13} + q^{15} - q^{17} - 8 q^{19} + O(q^{20})$$

## 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. 