# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("kt1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.kt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.kt1 463680kt1 $$[0, 0, 0, -141132, 19481744]$$ $$1626794704081/83462400$$ $$15949913024102400$$ $$$$ $$4718592$$ $$1.8669$$ $$\Gamma_0(N)$$-optimal
463680.kt2 463680kt2 $$[0, 0, 0, 89268, 76897424]$$ $$411664745519/13605414480$$ $$-2600035196841492480$$ $$$$ $$9437184$$ $$2.2135$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 463680.2.a.kt

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 6q^{11} - 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 