# Properties

 Label 188760.cg Number of curves $2$ Conductor $188760$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

## Elliptic curves in class 188760.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cg1 188760bq2 $$[0, 1, 0, -99829880, -271404080400]$$ $$22784591413352662/6597644551875$$ $$31860532709647126467840000$$ $$$$ $$72382464$$ $$3.5998$$
188760.cg2 188760bq1 $$[0, 1, 0, 16606000, -28099665552]$$ $$209741642018356/262704572325$$ $$-634310287082369281612800$$ $$$$ $$36191232$$ $$3.2533$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 188760.cg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 188760.cg do not have complex multiplication.

## Modular form 188760.2.a.cg

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4q^{7} + q^{9} + q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 