# Properties

 Label 8280.q Number of curves $2$ Conductor $8280$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.q1 8280p2 $$[0, 0, 0, -2187, 17766]$$ $$28697814/13225$$ $$533110118400$$ $$[2]$$ $$7680$$ $$0.94490$$
8280.q2 8280p1 $$[0, 0, 0, -1107, -13986]$$ $$7443468/115$$ $$2317870080$$ $$[2]$$ $$3840$$ $$0.59833$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8280.q do not have complex multiplication.

## Modular form8280.2.a.q

sage: E.q_eigenform(10)

$$q + q^{5} - 4 q^{11} + 4 q^{13} - 4 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.