# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("96.b1")

sage: E.isogeny_class()

## Elliptic curves in class 96a

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Modular form96.2.a.b

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. 