# Properties

 Label 377520hs Number of curves $4$ Conductor $377520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hs1")

sage: E.isogeny_class()

## Elliptic curves in class 377520hs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.hs4 377520hs1 $$[0, 1, 0, -2460, 165900]$$ $$-3631696/24375$$ $$-11054540640000$$ $$[2]$$ $$983040$$ $$1.1862$$ $$\Gamma_0(N)$$-optimal
377520.hs3 377520hs2 $$[0, 1, 0, -62960, 6046500]$$ $$15214885924/38025$$ $$68980333593600$$ $$[2, 2]$$ $$1966080$$ $$1.5328$$
377520.hs1 377520hs3 $$[0, 1, 0, -1006760, 388474260]$$ $$31103978031362/195$$ $$707490600960$$ $$[2]$$ $$3932160$$ $$1.8793$$
377520.hs2 377520hs4 $$[0, 1, 0, -87160, 945140]$$ $$20183398562/11567205$$ $$41967634958346240$$ $$[2]$$ $$3932160$$ $$1.8793$$

## Rank

sage: E.rank()

The elliptic curves in class 377520hs have rank $$0$$.

## Complex multiplication

The elliptic curves in class 377520hs do not have complex multiplication.

## Modular form 377520.2.a.hs

sage: E.q_eigenform(10)

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

## 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.