# Properties

 Label 153.b Number of curves 2 Conductor 153 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("153.b1")
sage: E.isogeny_class()

## Elliptic curves in class 153.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
153.b1 153b2 [0, 0, 1, -534, 4752] 3 48
153.b2 153b1 [0, 0, 1, 6, 27] 1 16 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 153.b have rank $$1$$.

## Modular form153.2.a.b

sage: E.q_eigenform(10)
$$q - 2q^{4} - 3q^{5} - 4q^{7} + 3q^{11} - q^{13} + 4q^{16} + q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 