# Properties

 Label 8820.a Number of curves $2$ Conductor $8820$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 8820.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8820.a1 8820r1 $$[0, 0, 0, -439383, 112169918]$$ $$-177953104/125$$ $$-6589582608672000$$ $$[]$$ $$90720$$ $$1.9716$$ $$\Gamma_0(N)$$-optimal
8820.a2 8820r2 $$[0, 0, 0, 424977, 476411222]$$ $$161017136/1953125$$ $$-102962228260500000000$$ $$[]$$ $$272160$$ $$2.5210$$

## Rank

sage: E.rank()

The elliptic curves in class 8820.a have rank $$0$$.

## Complex multiplication

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

## Modular form8820.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - 6 q^{11} - 2 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.