# Properties

 Label 84.b Number of curves 4 Conductor 84 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("84.b1")

sage: E.isogeny_class()

## Elliptic curves in class 84.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84.b1 84a4 [0, 1, 0, -1828, -30700]  36
84.b2 84a3 [0, 1, 0, -113, -516]  18
84.b3 84a2 [0, 1, 0, -28, -28]  12
84.b4 84a1 [0, 1, 0, 7, 0]  6 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 84.b have rank $$0$$.

## Modular form84.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - 6q^{11} + 2q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 