# Properties

 Label 8820.h Number of curves $4$ Conductor $8820$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8820.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8820.h1 8820a4 $$[0, 0, 0, -186543, 12428262]$$ $$1210991472/588245$$ $$348720711650922240$$ $$$$ $$82944$$ $$2.0596$$
8820.h2 8820a3 $$[0, 0, 0, -153468, 23124717]$$ $$10788913152/8575$$ $$317712018632400$$ $$$$ $$41472$$ $$1.7130$$
8820.h3 8820a2 $$[0, 0, 0, -98343, -11869858]$$ $$129348709488/6125$$ $$4980788064000$$ $$$$ $$27648$$ $$1.5103$$
8820.h4 8820a1 $$[0, 0, 0, -6468, -164983]$$ $$588791808/109375$$ $$5558915250000$$ $$$$ $$13824$$ $$1.1637$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8820.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8820.h do not have complex multiplication.

## Modular form8820.2.a.h

sage: E.q_eigenform(10)

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

## 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. 