# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1950.k1")

sage: E.isogeny_class()

## Elliptic curves in class 1950g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1950.k6 1950g1 [1, 0, 1, 374, 1148]  1536 $$\Gamma_0(N)$$-optimal
1950.k5 1950g2 [1, 0, 1, -1626, 9148] [2, 2] 3072
1950.k3 1950g3 [1, 0, 1, -14126, -640852] [2, 2] 6144
1950.k2 1950g4 [1, 0, 1, -21126, 1179148]  6144
1950.k1 1950g5 [1, 0, 1, -225376, -41200852]  12288
1950.k4 1950g6 [1, 0, 1, -2876, -1630852]  12288

## Rank

sage: E.rank()

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 