# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ck1 463680ck1 $$[0, 0, 0, -13548, 334672]$$ $$1439069689/579600$$ $$110763284889600$$ $$$$ $$1179648$$ $$1.3928$$ $$\Gamma_0(N)$$-optimal
463680.ck2 463680ck2 $$[0, 0, 0, 44052, 2431312]$$ $$49471280711/41992020$$ $$-8024799990251520$$ $$$$ $$2359296$$ $$1.7394$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 463680.2.a.ck

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 2q^{11} - 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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 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. 