# Properties

 Label 374850cm Number of curves $2$ Conductor $374850$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 374850cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374850.cm2 374850cm1 $$[1, -1, 0, 898308, 391027216]$$ $$59822347031/83966400$$ $$-112523006598975000000$$ $$[2]$$ $$10616832$$ $$2.5331$$ $$\Gamma_0(N)$$-optimal
374850.cm1 374850cm2 $$[1, -1, 0, -5716692, 3877132216]$$ $$15417797707369/4080067320$$ $$5467680428988526875000$$ $$[2]$$ $$21233664$$ $$2.8797$$

## Rank

sage: E.rank()

The elliptic curves in class 374850cm have rank $$1$$.

## Complex multiplication

The elliptic curves in class 374850cm do not have complex multiplication.

## Modular form 374850.2.a.cm

sage: E.q_eigenform(10)

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

## 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 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.