# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 4840.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4840.f1 4840g3 $$[0, 0, 0, -12947, 567006]$$ $$132304644/5$$ $$9070392320$$ $$[2]$$ $$5120$$ $$0.99673$$
4840.f2 4840g2 $$[0, 0, 0, -847, 7986]$$ $$148176/25$$ $$11337990400$$ $$[2, 2]$$ $$2560$$ $$0.65016$$
4840.f3 4840g1 $$[0, 0, 0, -242, -1331]$$ $$55296/5$$ $$141724880$$ $$[2]$$ $$1280$$ $$0.30359$$ $$\Gamma_0(N)$$-optimal
4840.f4 4840g4 $$[0, 0, 0, 1573, 45254]$$ $$237276/625$$ $$-1133799040000$$ $$[2]$$ $$5120$$ $$0.99673$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4840.2.a.f

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 3q^{9} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.