# Properties

 Label 424830.q Number of curves $2$ Conductor $424830$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 424830.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.q1 424830q2 $$[1, 1, 0, -532715873, 4703989857477]$$ $$1198345620520313/8268750000$$ $$115363492146750728868750000$$ $$[2]$$ $$240648192$$ $$3.8344$$ $$\Gamma_0(N)$$-optimal*
424830.q2 424830q1 $$[1, 1, 0, -12723953, 163316413653]$$ $$-16329068153/816480000$$ $$-11391320824547729113440000$$ $$[2]$$ $$120324096$$ $$3.4879$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 424830.q1.

## Rank

sage: E.rank()

The elliptic curves in class 424830.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 424830.q do not have complex multiplication.

## Modular form 424830.2.a.q

sage: E.q_eigenform(10)

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

## 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.