# Properties

 Label 74970.ch Number of curves $2$ Conductor $74970$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ch1")

sage: E.isogeny_class()

## Elliptic curves in class 74970.ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74970.ch1 74970cy2 $$[1, -1, 1, -228668, 31062791]$$ $$15417797707369/4080067320$$ $$349931547455265720$$ $$[2]$$ $$884736$$ $$2.0750$$
74970.ch2 74970cy1 $$[1, -1, 1, 35932, 3121031]$$ $$59822347031/83966400$$ $$-7201472422334400$$ $$[2]$$ $$442368$$ $$1.7284$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 74970.ch have rank $$1$$.

## Complex multiplication

The elliptic curves in class 74970.ch do not have complex multiplication.

## Modular form 74970.2.a.ch

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 2q^{11} + 2q^{13} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.