# Properties

 Label 374850la Number of curves $4$ Conductor $374850$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("la1")

sage: E.isogeny_class()

## Elliptic curves in class 374850la

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374850.la4 374850la1 $$[1, -1, 1, 10795, 116650797]$$ $$103823/4386816$$ $$-5878752997824000000$$ $$[2]$$ $$9437184$$ $$2.2804$$ $$\Gamma_0(N)$$-optimal
374850.la3 374850la2 $$[1, -1, 1, -3517205, 2494522797]$$ $$3590714269297/73410624$$ $$98377257197961000000$$ $$[2, 2]$$ $$18874368$$ $$2.6270$$
374850.la1 374850la3 $$[1, -1, 1, -55996205, 161295976797]$$ $$14489843500598257/6246072$$ $$8370333858229875000$$ $$[2]$$ $$37748736$$ $$2.9735$$
374850.la2 374850la4 $$[1, -1, 1, -7486205, -4165459203]$$ $$34623662831857/14438442312$$ $$19348893599726746125000$$ $$[2]$$ $$37748736$$ $$2.9735$$

## Rank

sage: E.rank()

The elliptic curves in class 374850la have rank $$2$$.

## Complex multiplication

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

## Modular form 374850.2.a.la

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 6q^{13} + q^{16} - q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.