# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.bb1 1950y2 $$[1, 0, 0, -227906263, -1324307174983]$$ $$-134057911417971280740025/1872$$ $$-18281250000$$ $$[]$$ $$168000$$ $$2.9487$$
1950.bb2 1950y1 $$[1, 0, 0, -355303, -89334583]$$ $$-198417696411528597145/22989483914821632$$ $$-574737097870540800$$ $$$$ $$33600$$ $$2.1440$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.bb

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 