# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.r1 1950t2 $$[1, 1, 1, -1638, 22281]$$ $$248858189/27378$$ $$53472656250$$ $$$$ $$2560$$ $$0.79197$$
1950.r2 1950t1 $$[1, 1, 1, -388, -2719]$$ $$3307949/468$$ $$914062500$$ $$$$ $$1280$$ $$0.44539$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.r

sage: E.q_eigenform(10)

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