# Properties

 Label 435344j Number of curves $2$ Conductor $435344$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 435344j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.j2 435344j1 $$[0, 1, 0, 93232, -51510380]$$ $$4533086375/60669952$$ $$-1199481939325616128$$ $$$$ $$6322176$$ $$2.1498$$ $$\Gamma_0(N)$$-optimal*
435344.j1 435344j2 $$[0, 1, 0, -1637328, -755502188]$$ $$24553362849625/1755162752$$ $$34700637666584035328$$ $$$$ $$12644352$$ $$2.4964$$ $$\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 435344j1.

## Rank

sage: E.rank()

The elliptic curves in class 435344j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 435344j do not have complex multiplication.

## Modular form 435344.2.a.j

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 4q^{11} + 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 