# Properties

 Label 178.b Number of curves 2 Conductor 178 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("178.b1")

sage: E.isogeny_class()

## Elliptic curves in class 178.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
178.b1 178a2 [1, 0, 0, -554, -5068] [] 96
178.b2 178a1 [1, 0, 0, 6, -28]  32 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 178.b have rank $$0$$.

## Modular form178.2.a.b

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 3q^{5} + q^{6} - 4q^{7} + q^{8} - 2q^{9} + 3q^{10} - 6q^{11} + q^{12} + 2q^{13} - 4q^{14} + 3q^{15} + q^{16} + 3q^{17} - 2q^{18} + 5q^{19} + O(q^{20})$$

## 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. 