# Properties

 Label 38640.ce Number of curves $2$ Conductor $38640$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 38640.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.ce1 38640cm1 $$[0, 1, 0, -60398616, 180563933844]$$ $$5949010462538271898545049/3314625947988102720$$ $$13576707882959268741120$$ $$$$ $$5091840$$ $$3.1943$$ $$\Gamma_0(N)$$-optimal
38640.ce2 38640cm2 $$[0, 1, 0, -49642136, 246922810260]$$ $$-3303050039017428591035929/4519896503737558217400$$ $$-18513496079309038458470400$$ $$$$ $$10183680$$ $$3.5409$$

## Rank

sage: E.rank()

The elliptic curves in class 38640.ce have rank $$0$$.

## Complex multiplication

The elliptic curves in class 38640.ce do not have complex multiplication.

## Modular form 38640.2.a.ce

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} + 4q^{19} + O(q^{20})$$ ## 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. 