# Properties

 Label 9744.l Number of curves $6$ Conductor $9744$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9744.l1")

sage: E.isogeny_class()

## Elliptic curves in class 9744.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9744.l1 9744q3 [0, 1, 0, -3273984, -2281239180] [2] 98304
9744.l2 9744q5 [0, 1, 0, -679504, 175033940] [4] 196608
9744.l3 9744q4 [0, 1, 0, -208544, -34260684] [2, 4] 98304
9744.l4 9744q2 [0, 1, 0, -204624, -35695404] [2, 2] 49152
9744.l5 9744q1 [0, 1, 0, -12544, -583180] [2] 24576 $$\Gamma_0(N)$$-optimal
9744.l6 9744q6 [0, 1, 0, 199696, -151670508] [4] 196608

## Rank

sage: E.rank()

The elliptic curves in class 9744.l have rank $$0$$.

## Modular form9744.2.a.l

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.