# Properties

 Label 3920.h Number of curves $4$ Conductor $3920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.h1 3920bf3 $$[0, 1, 0, -2025, -35750]$$ $$488095744/125$$ $$235298000$$ $$[2]$$ $$2160$$ $$0.59231$$
3920.h2 3920bf4 $$[0, 1, 0, -1780, -44472]$$ $$-20720464/15625$$ $$-470596000000$$ $$[2]$$ $$4320$$ $$0.93888$$
3920.h3 3920bf1 $$[0, 1, 0, -65, 118]$$ $$16384/5$$ $$9411920$$ $$[2]$$ $$720$$ $$0.043005$$ $$\Gamma_0(N)$$-optimal
3920.h4 3920bf2 $$[0, 1, 0, 180, 1000]$$ $$21296/25$$ $$-752953600$$ $$[2]$$ $$1440$$ $$0.38958$$

## Rank

sage: E.rank()

The elliptic curves in class 3920.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3920.h do not have complex multiplication.

## Modular form3920.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.