# Properties

 Label 4624f Number of curves 4 Conductor 4624 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4624.a1")

sage: E.isogeny_class()

## Elliptic curves in class 4624f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4624.a4 4624f1 [0, 1, 0, -13968, -398060] [2] 13824 $$\Gamma_0(N)$$-optimal
4624.a3 4624f2 [0, 1, 0, -198928, -34208748] [2] 27648
4624.a2 4624f3 [0, 1, 0, -476368, 126373524] [2] 41472
4624.a1 4624f4 [0, 1, 0, -522608, 100312660] [2] 82944

## Rank

sage: E.rank()

The elliptic curves in class 4624f have rank $$0$$.

## Modular form4624.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{7} + q^{9} + 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.