# Properties

 Label 8624.y Number of curves $2$ Conductor $8624$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 8624.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8624.y1 8624t2 $$[0, -1, 0, -44704, 1440384]$$ $$59776471/29282$$ $$4839974175432704$$ $$$$ $$43008$$ $$1.7029$$
8624.y2 8624t1 $$[0, -1, 0, 10176, 167168]$$ $$704969/484$$ $$-79999573147648$$ $$$$ $$21504$$ $$1.3564$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 8624.y do not have complex multiplication.

## Modular form8624.2.a.y

sage: E.q_eigenform(10)

$$q + 2 q^{3} - 2 q^{5} + q^{9} - q^{11} + 2 q^{13} - 4 q^{15} + 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 