# Properties

 Label 468270.v Number of curves $2$ Conductor $468270$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 468270.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
468270.v1 468270v2 $$[1, -1, 0, -258660, -48951864]$$ $$1481933914201/53916840$$ $$69631871849697960$$ $$$$ $$6451200$$ $$2.0016$$
468270.v2 468270v1 $$[1, -1, 0, -40860, 2144016]$$ $$5841725401/1857600$$ $$2399030899214400$$ $$$$ $$3225600$$ $$1.6550$$ $$\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 0 curves highlighted, and conditionally curve 468270.v1.

## Rank

sage: E.rank()

The elliptic curves in class 468270.v have rank $$2$$.

## Complex multiplication

The elliptic curves in class 468270.v do not have complex multiplication.

## Modular form 468270.2.a.v

sage: E.q_eigenform(10)

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