# Properties

 Label 9408p Number of curves $6$ Conductor $9408$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.n1")

sage: E.isogeny_class()

## Elliptic curves in class 9408p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.n5 9408p1 [0, -1, 0, -12609, -1199295] [2] 36864 $$\Gamma_0(N)$$-optimal
9408.n4 9408p2 [0, -1, 0, -263489, -51927231] [2, 2] 73728
9408.n1 9408p3 [0, -1, 0, -4214849, -3329185215] [2] 147456
9408.n3 9408p4 [0, -1, 0, -326209, -25271231] [2, 2] 147456
9408.n2 9408p5 [0, -1, 0, -2866369, 1850890945] [2] 294912
9408.n6 9408p6 [0, -1, 0, 1210431, -196452927] [2] 294912

## Rank

sage: E.rank()

The elliptic curves in class 9408p have rank $$0$$.

## Modular form9408.2.a.n

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.