# Properties

 Label 56.b Number of curves 2 Conductor 56 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("56.b1")

sage: E.isogeny_class()

## Elliptic curves in class 56.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
56.b1 56b2 [0, -1, 0, -40, -84]  8
56.b2 56b1 [0, -1, 0, 0, -4]  4 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 56.b have rank $$0$$.

## Modular form56.2.a.b

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{5} + q^{7} + q^{9} - 8q^{15} - 2q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 