Properties

 Label 212160go Number of curves $2$ Conductor $212160$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("go1")

sage: E.isogeny_class()

Elliptic curves in class 212160go

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.cy1 212160go1 $$[0, -1, 0, -1124065, 458394337]$$ $$2396726313900986596/4154072495625$$ $$272241295073280000$$ $$[2]$$ $$2949120$$ $$2.2393$$ $$\Gamma_0(N)$$-optimal
212160.cy2 212160go2 $$[0, -1, 0, -772545, 749945025]$$ $$-389032340685029858/1627263833203125$$ $$-213288725145600000000$$ $$[2]$$ $$5898240$$ $$2.5859$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 212160.2.a.go

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 Cremona 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 Cremona labels.