# Properties

 Label 950.d Number of curves $3$ Conductor $950$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 950.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.d1 950e3 $$[1, 1, 1, -2138, -306969]$$ $$-69173457625/2550136832$$ $$-39845888000000$$ $$[]$$ $$2592$$ $$1.2899$$
950.d2 950e1 $$[1, 1, 1, -388, 2781]$$ $$-413493625/152$$ $$-2375000$$ $$[]$$ $$288$$ $$0.19128$$ $$\Gamma_0(N)$$-optimal
950.d3 950e2 $$[1, 1, 1, 237, 11281]$$ $$94196375/3511808$$ $$-54872000000$$ $$[]$$ $$864$$ $$0.74058$$

## Rank

sage: E.rank()

The elliptic curves in class 950.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 950.d do not have complex multiplication.

## Modular form950.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} - 2q^{9} - 6q^{11} - q^{12} - 5q^{13} + q^{14} + q^{16} - 3q^{17} - 2q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 