# Properties

 Label 4830.s Number of curves $4$ Conductor $4830$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4830.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.s1 4830t3 $$[1, 1, 1, -4491, -117711]$$ $$10017490085065009/235066440$$ $$235066440$$ $$$$ $$6144$$ $$0.71829$$
4830.s2 4830t4 $$[1, 1, 1, -1211, 14033]$$ $$196416765680689/22365315000$$ $$22365315000$$ $$$$ $$6144$$ $$0.71829$$
4830.s3 4830t2 $$[1, 1, 1, -291, -1791]$$ $$2725812332209/373262400$$ $$373262400$$ $$[2, 2]$$ $$3072$$ $$0.37171$$
4830.s4 4830t1 $$[1, 1, 1, 29, -127]$$ $$2691419471/9891840$$ $$-9891840$$ $$$$ $$1536$$ $$0.025141$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4830.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} - 2q^{13} + q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20})$$ ## 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. 