# Properties

 Label 182070.ci Number of curves $2$ Conductor $182070$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 182070.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.ci1 182070bn2 $$[1, -1, 1, -1348673, -443775463]$$ $$15417797707369/4080067320$$ $$71794038810174763320$$ $$$$ $$5308416$$ $$2.5186$$
182070.ci2 182070bn1 $$[1, -1, 1, 211927, -44886103]$$ $$59822347031/83966400$$ $$-1477496940013886400$$ $$$$ $$2654208$$ $$2.1720$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 182070.ci have rank $$1$$.

## Complex multiplication

The elliptic curves in class 182070.ci do not have complex multiplication.

## Modular form 182070.2.a.ci

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2q^{11} - 2q^{13} - q^{14} + q^{16} - 4q^{19} + O(q^{20})$$ ## 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. 