# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.w1 1950v4 $$[1, 0, 0, -518488, 143656592]$$ $$986551739719628473/111045168$$ $$1735080750000$$ $$$$ $$20480$$ $$1.7728$$
1950.w2 1950v3 $$[1, 0, 0, -58488, -1851408]$$ $$1416134368422073/725251155408$$ $$11332049303250000$$ $$$$ $$20480$$ $$1.7728$$
1950.w3 1950v2 $$[1, 0, 0, -32488, 2230592]$$ $$242702053576633/2554695936$$ $$39917124000000$$ $$[2, 2]$$ $$10240$$ $$1.4262$$
1950.w4 1950v1 $$[1, 0, 0, -488, 86592]$$ $$-822656953/207028224$$ $$-3234816000000$$ $$$$ $$5120$$ $$1.0796$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.w

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 