# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.d1 1950d2 $$[1, 1, 0, -88075, 9992125]$$ $$38686490446661/141927552$$ $$277202250000000$$ $$$$ $$17920$$ $$1.6317$$
1950.d2 1950d1 $$[1, 1, 0, -8075, -7875]$$ $$29819839301/17252352$$ $$33696000000000$$ $$$$ $$8960$$ $$1.2852$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1950.2.a.d

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 