# Properties

 Label 1950.k Number of curves $6$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1950.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.k1 1950g5 $$[1, 0, 1, -225376, -41200852]$$ $$81025909800741361/11088090$$ $$173251406250$$ $$$$ $$12288$$ $$1.5688$$
1950.k2 1950g4 $$[1, 0, 1, -21126, 1179148]$$ $$66730743078481/60937500$$ $$952148437500$$ $$$$ $$6144$$ $$1.2222$$
1950.k3 1950g3 $$[1, 0, 1, -14126, -640852]$$ $$19948814692561/231344100$$ $$3614751562500$$ $$[2, 2]$$ $$6144$$ $$1.2222$$
1950.k4 1950g6 $$[1, 0, 1, -2876, -1630852]$$ $$-168288035761/73415764890$$ $$-1147121326406250$$ $$$$ $$12288$$ $$1.5688$$
1950.k5 1950g2 $$[1, 0, 1, -1626, 9148]$$ $$30400540561/15210000$$ $$237656250000$$ $$[2, 2]$$ $$3072$$ $$0.87564$$
1950.k6 1950g1 $$[1, 0, 1, 374, 1148]$$ $$371694959/249600$$ $$-3900000000$$ $$$$ $$1536$$ $$0.52907$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1950.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1950.k do not have complex multiplication.

## Modular form1950.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} - q^{13} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 