# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 4830.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.q1 4830p2 $$[1, 0, 1, -423, 1828]$$ $$8341959848041/3327411150$$ $$3327411150$$ $$$$ $$3840$$ $$0.52532$$
4830.q2 4830p1 $$[1, 0, 1, -193, -1024]$$ $$789145184521/17996580$$ $$17996580$$ $$$$ $$1920$$ $$0.17875$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4830.2.a.q

sage: E.q_eigenform(10)

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