# Properties

 Label 8280.g Number of curves $6$ Conductor $8280$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.g1 8280i5 $$[0, 0, 0, -7837923, 8148740222]$$ $$35667215800077781442/1427217706746225$$ $$2130824618430459955200$$ $$[2]$$ $$344064$$ $$2.8590$$
8280.g2 8280i3 $$[0, 0, 0, -1276923, -384496378]$$ $$308453964046598884/92949363050625$$ $$69386327719839360000$$ $$[2, 2]$$ $$172032$$ $$2.5124$$
8280.g3 8280i2 $$[0, 0, 0, -1164423, -483563878]$$ $$935596404100595536/150641015625$$ $$28113228900000000$$ $$[2, 2]$$ $$86016$$ $$2.1658$$
8280.g4 8280i1 $$[0, 0, 0, -1164378, -483603127]$$ $$14967807005098080256/388125$$ $$4527090000$$ $$[2]$$ $$43008$$ $$1.8192$$ $$\Gamma_0(N)$$-optimal
8280.g5 8280i4 $$[0, 0, 0, -1052643, -580119442]$$ $$-172798332611391364/94757080078125$$ $$-70735781250000000000$$ $$[2]$$ $$172032$$ $$2.5124$$
8280.g6 8280i6 $$[0, 0, 0, 3484077, -2577412978]$$ $$3132776881711582558/3735130619961225$$ $$-5576520134557149235200$$ $$[2]$$ $$344064$$ $$2.8590$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8280.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.