# Properties

 Label 1950.y Number of curves $4$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("y1")

E.isogeny_class()

## Elliptic curves in class 1950.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.y1 1950w3 $$[1, 0, 0, -12088, -512458]$$ $$12501706118329/2570490$$ $$40163906250$$ $$$$ $$3072$$ $$1.0318$$
1950.y2 1950w2 $$[1, 0, 0, -838, -6208]$$ $$4165509529/1368900$$ $$21389062500$$ $$[2, 2]$$ $$1536$$ $$0.68518$$
1950.y3 1950w1 $$[1, 0, 0, -338, 2292]$$ $$273359449/9360$$ $$146250000$$ $$$$ $$768$$ $$0.33860$$ $$\Gamma_0(N)$$-optimal
1950.y4 1950w4 $$[1, 0, 0, 2412, -41958]$$ $$99317171591/106616250$$ $$-1665878906250$$ $$$$ $$3072$$ $$1.0318$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.y

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 