# Properties

 Label 46800.k Number of curves $4$ Conductor $46800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 46800.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.k1 46800cc4 $$[0, 0, 0, -1809675, -561255750]$$ $$520300455507/193072360$$ $$243215568760320000000$$ $$$$ $$1990656$$ $$2.6117$$
46800.k2 46800cc2 $$[0, 0, 0, -1599675, -778745750]$$ $$261984288445803/42250$$ $$73008000000000$$ $$$$ $$663552$$ $$2.0624$$
46800.k3 46800cc1 $$[0, 0, 0, -99675, -12245750]$$ $$-63378025803/812500$$ $$-1404000000000000$$ $$$$ $$331776$$ $$1.7158$$ $$\Gamma_0(N)$$-optimal
46800.k4 46800cc3 $$[0, 0, 0, 350325, -62295750]$$ $$3774555693/3515200$$ $$-4428139622400000000$$ $$$$ $$995328$$ $$2.2651$$

## Rank

sage: E.rank()

The elliptic curves in class 46800.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46800.k do not have complex multiplication.

## Modular form 46800.2.a.k

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 