# Properties

 Label 1950.b Number of curves $4$ Conductor $1950$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.b1 1950a4 $$[1, 1, 0, -29900, -1901250]$$ $$189208196468929/10860320250$$ $$169692503906250$$ $$$$ $$6912$$ $$1.4845$$
1950.b2 1950a2 $$[1, 1, 0, -5150, 139500]$$ $$967068262369/4928040$$ $$77000625000$$ $$$$ $$2304$$ $$0.93524$$
1950.b3 1950a1 $$[1, 1, 0, -150, 4500]$$ $$-24137569/561600$$ $$-8775000000$$ $$$$ $$1152$$ $$0.58866$$ $$\Gamma_0(N)$$-optimal
1950.b4 1950a3 $$[1, 1, 0, 1350, -120000]$$ $$17394111071/411937500$$ $$-6436523437500$$ $$$$ $$3456$$ $$1.1380$$

## Rank

sage: E.rank()

The elliptic curves in class 1950.b have rank $$1$$.

## Complex multiplication

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

## Modular form1950.2.a.b

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 