# Properties

 Label 8280.p Number of curves $4$ Conductor $8280$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 8280.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.p1 8280l3 $$[0, 0, 0, -9507, -351106]$$ $$63649751618/1164375$$ $$1738402560000$$ $$[2]$$ $$12288$$ $$1.1435$$
8280.p2 8280l2 $$[0, 0, 0, -1227, 8246]$$ $$273671716/119025$$ $$88851686400$$ $$[2, 2]$$ $$6144$$ $$0.79696$$
8280.p3 8280l1 $$[0, 0, 0, -1047, 13034]$$ $$680136784/345$$ $$64385280$$ $$[2]$$ $$3072$$ $$0.45039$$ $$\Gamma_0(N)$$-optimal
8280.p4 8280l4 $$[0, 0, 0, 4173, 61166]$$ $$5382838942/4197615$$ $$-6267005614080$$ $$[2]$$ $$12288$$ $$1.1435$$

## Rank

sage: E.rank()

The elliptic curves in class 8280.p have rank $$0$$.

## Complex multiplication

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

## Modular form8280.2.a.p

sage: E.q_eigenform(10)

$$q + q^{5} - 4 q^{11} + 2 q^{13} - 2 q^{17} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.