# Properties

 Label 96b Number of curves 4 Conductor 96 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("96.a1")

sage: E.isogeny_class()

## Elliptic curves in class 96b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96.a3 96b1 [0, -1, 0, -2, 0] [2, 2] 4 $$\Gamma_0(N)$$-optimal
96.a1 96b2 [0, -1, 0, -32, -60]  8
96.a2 96b3 [0, -1, 0, -17, 33]  8
96.a4 96b4 [0, -1, 0, 8, -8]  8

## Rank

sage: E.rank()

The elliptic curves in class 96b have rank $$0$$.

## Modular form96.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + 4q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 