# Properties

 Label 4680g Number of curves $4$ Conductor $4680$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4680g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4680.k4 4680g1 $$[0, 0, 0, -183, -3382]$$ $$-3631696/24375$$ $$-4548960000$$ $$$$ $$3072$$ $$0.53654$$ $$\Gamma_0(N)$$-optimal
4680.k3 4680g2 $$[0, 0, 0, -4683, -123082]$$ $$15214885924/38025$$ $$28385510400$$ $$[2, 2]$$ $$6144$$ $$0.88311$$
4680.k1 4680g3 $$[0, 0, 0, -74883, -7887202]$$ $$31103978031362/195$$ $$291133440$$ $$$$ $$12288$$ $$1.2297$$
4680.k2 4680g4 $$[0, 0, 0, -6483, -19762]$$ $$20183398562/11567205$$ $$17269744527360$$ $$$$ $$12288$$ $$1.2297$$

## Rank

sage: E.rank()

The elliptic curves in class 4680g have rank $$1$$.

## Complex multiplication

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

## Modular form4680.2.a.g

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} - 4q^{11} + q^{13} - 6q^{17} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 