# Properties

 Label 463680kh Number of curves $2$ Conductor $463680$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("kh1")

sage: E.isogeny_class()

## Elliptic curves in class 463680kh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.kh1 463680kh1 $$[0, 0, 0, -3132, -18576]$$ $$10536048/5635$$ $$1817210142720$$ $$$$ $$737280$$ $$1.0436$$ $$\Gamma_0(N)$$-optimal
463680.kh2 463680kh2 $$[0, 0, 0, 11988, -145584]$$ $$147704148/92575$$ $$-119416666521600$$ $$$$ $$1474560$$ $$1.3902$$

## Rank

sage: E.rank()

The elliptic curves in class 463680kh have rank $$0$$.

## Complex multiplication

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

## Modular form 463680.2.a.kh

sage: E.q_eigenform(10)

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