# Properties

 Label 435344.i Number of curves $2$ Conductor $435344$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 435344.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.i1 435344i2 $$[0, 1, 0, -265048, 35763924]$$ $$104154702625/32188247$$ $$636381267205419008$$ $$[2]$$ $$5160960$$ $$2.1208$$ $$\Gamma_0(N)$$-optimal*
435344.i2 435344i1 $$[0, 1, 0, 45912, 3797236]$$ $$541343375/625807$$ $$-12372585921998848$$ $$[2]$$ $$2580480$$ $$1.7742$$ $$\Gamma_0(N)$$-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 435344.i1.

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 435344.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} - 4q^{11} + 8q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.