# Properties

 Label 4851j Number of curves 4 Conductor 4851 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4851.b1")

sage: E.isogeny_class()

## Elliptic curves in class 4851j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4851.b3 4851j1 [1, -1, 1, -2876, -58138] [2] 3456 $$\Gamma_0(N)$$-optimal
4851.b2 4851j2 [1, -1, 1, -5081, 45056] [2, 2] 6912
4851.b1 4851j3 [1, -1, 1, -64616, 6331952] [2] 13824
4851.b4 4851j4 [1, -1, 1, 19174, 336116] [2] 13824

## Rank

sage: E.rank()

The elliptic curves in class 4851j have rank $$1$$.

## Modular form4851.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 2q^{5} + 3q^{8} + 2q^{10} - q^{11} + 2q^{13} - q^{16} - 2q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.