# Properties

 Label 4840.f Number of curves 4 Conductor 4840 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4840.f1")

sage: E.isogeny_class()

## Elliptic curves in class 4840.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4840.f1 4840g3 [0, 0, 0, -12947, 567006]  5120
4840.f2 4840g2 [0, 0, 0, -847, 7986] [2, 2] 2560
4840.f3 4840g1 [0, 0, 0, -242, -1331]  1280 $$\Gamma_0(N)$$-optimal
4840.f4 4840g4 [0, 0, 0, 1573, 45254]  5120

## Rank

sage: E.rank()

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

## 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. 