# Properties

 Label 463680.ey Number of curves $2$ Conductor $463680$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ey1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.ey

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ey1 463680ey1 $$[0, 0, 0, -315302508, -900998410832]$$ $$489781415227546051766883/233890092903563264000$$ $$1655447881881015583506432000$$ $$$$ $$198180864$$ $$3.9167$$ $$\Gamma_0(N)$$-optimal
463680.ey2 463680ey2 $$[0, 0, 0, 1131732372, -6852942279248]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-113058713414394313703424000000$$ $$$$ $$396361728$$ $$4.2633$$

## Rank

sage: E.rank()

The elliptic curves in class 463680.ey have rank $$1$$.

## Complex multiplication

The elliptic curves in class 463680.ey do not have complex multiplication.

## Modular form 463680.2.a.ey

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 2q^{11} + 6q^{13} - 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 