# Properties

 Label 8624.j Number of curves 3 Conductor 8624 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8624.j1")

sage: E.isogeny_class()

## Elliptic curves in class 8624.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8624.j1 8624r3 [0, -1, 0, -6131141, -5841282131] [] 72000
8624.j2 8624r2 [0, -1, 0, -8101, -505651] [] 14400
8624.j3 8624r1 [0, -1, 0, -261, 3949] [] 2880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8624.j have rank $$1$$.

## Modular form8624.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2q^{9} - q^{11} - 4q^{13} + q^{15} + 2q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.