# Properties

 Label 950.b Number of curves $2$ Conductor $950$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 950.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.b1 950a2 $$[1, 0, 1, -1751, -31352]$$ $$-37966934881/4952198$$ $$-77378093750$$ $$[]$$ $$800$$ $$0.82250$$
950.b2 950a1 $$[1, 0, 1, -1, 148]$$ $$-1/608$$ $$-9500000$$ $$[]$$ $$160$$ $$0.017785$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form950.2.a.b

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 