# Properties

 Label 1950.u Number of curves $2$ Conductor $1950$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.u1 1950u2 $$[1, 1, 1, -9098, -311569]$$ $$666276475992821/58199166792$$ $$7274895849000$$ $$$$ $$6144$$ $$1.2085$$
1950.u2 1950u1 $$[1, 1, 1, -8898, -326769]$$ $$623295446073461/5458752$$ $$682344000$$ $$$$ $$3072$$ $$0.86193$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.u

sage: E.q_eigenform(10)

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

## 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. 