# Properties

 Label 64757.h Number of curves $4$ Conductor $64757$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 64757.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64757.h1 64757e4 $$[1, -1, 0, -44872133, 115693155606]$$ $$16798320881842096017/2132227789307$$ $$1268298814764078028547$$ $$[4]$$ $$4515840$$ $$3.0712$$
64757.h2 64757e3 $$[1, -1, 0, -17800343, -27720846980]$$ $$1048626554636928177/48569076788309$$ $$28890019553125973354189$$ $$[2]$$ $$4515840$$ $$3.0712$$
64757.h3 64757e2 $$[1, -1, 0, -3044998, 1479980775]$$ $$5249244962308257/1448621666569$$ $$861673950581127255649$$ $$[2, 2]$$ $$2257920$$ $$2.7246$$
64757.h4 64757e1 $$[1, -1, 0, 491407, 150999776]$$ $$22062729659823/29354283343$$ $$-17460612303658242103$$ $$[2]$$ $$1128960$$ $$2.3780$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 64757.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 64757.h do not have complex multiplication.

## Modular form 64757.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 3q^{9} - 2q^{10} + q^{11} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.