# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 435344.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.c1 435344c2 $$[0, 1, 0, -21161560, 37460475924]$$ $$53008645999484449/2060047808$$ $$40728401101146816512$$ $$[2]$$ $$40255488$$ $$2.8473$$ $$\Gamma_0(N)$$-optimal*
435344.c2 435344c1 $$[0, 1, 0, -1260120, 642811924]$$ $$-11192824869409/2563305472$$ $$-50678111936507281408$$ $$[2]$$ $$20127744$$ $$2.5007$$ $$\Gamma_0(N)$$-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.c1.

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 435344.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{5} - q^{7} + q^{9} - 4q^{11} + 8q^{15} + 8q^{19} + O(q^{20})$$

## 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.