# Properties

 Label 4680.s Number of curves $4$ Conductor $4680$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("s1")

E.isogeny_class()

## Elliptic curves in class 4680.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4680.s1 4680i3 $$[0, 0, 0, -69267, -6999874]$$ $$49235161015876/137109375$$ $$102351600000000$$ $$[2]$$ $$12288$$ $$1.5608$$
4680.s2 4680i4 $$[0, 0, 0, -64587, 6294134]$$ $$39914580075556/172718325$$ $$128933538739200$$ $$[2]$$ $$12288$$ $$1.5608$$
4680.s3 4680i2 $$[0, 0, 0, -6087, -12166]$$ $$133649126224/77000625$$ $$14370164640000$$ $$[2, 2]$$ $$6144$$ $$1.2142$$
4680.s4 4680i1 $$[0, 0, 0, 1518, -1519]$$ $$33165879296/19278675$$ $$-224866465200$$ $$[4]$$ $$3072$$ $$0.86767$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4680.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4680.s do not have complex multiplication.

## Modular form4680.2.a.s

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.