# Properties

 Label 435344.d Number of curves $2$ Conductor $435344$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 435344.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.d1 435344d2 $$[0, 1, 0, -63600, 2653444]$$ $$5756278756/2705927$$ $$13374456624069632$$ $$[2]$$ $$4423680$$ $$1.7886$$ $$\Gamma_0(N)$$-optimal*
435344.d2 435344d1 $$[0, 1, 0, 14140, 321244]$$ $$253012016/181447$$ $$-224207363231488$$ $$[2]$$ $$2211840$$ $$1.4420$$ $$\Gamma_0(N)$$-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.d1.

## Rank

sage: E.rank()

The elliptic curves in class 435344.d have rank $$1$$.

## Complex multiplication

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

## Modular form 435344.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{5} + q^{7} + q^{9} + 4q^{11} + 8q^{15} - 4q^{17} + O(q^{20})$$

## 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.