# Properties

 Label 8280.v Number of curves $4$ Conductor $8280$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.v1 8280v3 $$[0, 0, 0, -22107, -1265146]$$ $$1600610497636/9315$$ $$6953610240$$ $$$$ $$14336$$ $$1.0786$$
8280.v2 8280v2 $$[0, 0, 0, -1407, -19006]$$ $$1650587344/119025$$ $$22212921600$$ $$[2, 2]$$ $$7168$$ $$0.73198$$
8280.v3 8280v1 $$[0, 0, 0, -282, 1469]$$ $$212629504/43125$$ $$503010000$$ $$$$ $$3584$$ $$0.38541$$ $$\Gamma_0(N)$$-optimal
8280.v4 8280v4 $$[0, 0, 0, 1293, -83266]$$ $$320251964/4197615$$ $$-3133502807040$$ $$$$ $$14336$$ $$1.0786$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8280.2.a.v

sage: E.q_eigenform(10)

$$q + q^{5} + 4 q^{7} - 4 q^{11} + 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 