# Properties

 Label 4840.e Number of curves $4$ Conductor $4840$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

## Elliptic curves in class 4840.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4840.e1 4840h3 $$[0, 0, 0, -913187, 17284366]$$ $$46424454082884/26794860125$$ $$48607978698654848000$$ $$[2]$$ $$138240$$ $$2.4671$$
4840.e2 4840h2 $$[0, 0, 0, -610687, -183031134]$$ $$55537159171536/228765625$$ $$103749698404000000$$ $$[2, 2]$$ $$69120$$ $$2.1205$$
4840.e3 4840h1 $$[0, 0, 0, -610082, -183413131]$$ $$885956203616256/15125$$ $$428717762000$$ $$[2]$$ $$34560$$ $$1.7739$$ $$\Gamma_0(N)$$-optimal
4840.e4 4840h4 $$[0, 0, 0, -317867, -358898826]$$ $$-1957960715364/29541015625$$ $$-53589720250000000000$$ $$[2]$$ $$138240$$ $$2.4671$$

## Rank

sage: E.rank()

The elliptic curves in class 4840.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4840.e do not have complex multiplication.

## Modular form4840.2.a.e

sage: E.q_eigenform(10)

$$q + q^{5} - 4 q^{7} - 3 q^{9} - 6 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.