# Properties

 Label 1950.z Number of curves $2$ Conductor $1950$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("z1")

E.isogeny_class()

## Elliptic curves in class 1950.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.z1 1950ba2 $$[1, 0, 0, -4013, -16983]$$ $$3659383421/2056392$$ $$4016390625000$$ $$[2]$$ $$3840$$ $$1.1086$$
1950.z2 1950ba1 $$[1, 0, 0, 987, -1983]$$ $$54439939/32448$$ $$-63375000000$$ $$[2]$$ $$1920$$ $$0.76201$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} + 2 q^{11} + q^{12} - q^{13} + 2 q^{14} + q^{16} + 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.