# Properties

 Label 37.b Number of curves 3 Conductor 37 CM no Rank 0 Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("37.b1")
sage: E.isogeny_class()

## Elliptic curves in class 37.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
37.b1 37b2 [0, 1, 1, -1873, -31833] 1 6
37.b2 37b1 [0, 1, 1, -23, -50] 3 2 $$\Gamma_0(N)$$-optimal
37.b3 37b3 [0, 1, 1, -3, 1] 3 6

## Rank

sage: E.rank()

The elliptic curves in class 37.b have rank $$0$$.

## Modular form37.2.a.b

sage: E.q_eigenform(10)
$$q + q^{3} - 2q^{4} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} - 4q^{13} + 4q^{16} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 