# Properties

 Label 4830.y Number of curves $2$ Conductor $4830$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 4830.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.y1 4830z1 $$[1, 1, 1, -245, 1307]$$ $$1626794704081/83462400$$ $$83462400$$ $$$$ $$3072$$ $$0.27788$$ $$\Gamma_0(N)$$-optimal
4830.y2 4830z2 $$[1, 1, 1, 155, 5627]$$ $$411664745519/13605414480$$ $$-13605414480$$ $$$$ $$6144$$ $$0.62445$$

## Rank

sage: E.rank()

The elliptic curves in class 4830.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4830.y do not have complex multiplication.

## Modular form4830.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 6q^{11} - q^{12} + q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} - 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 