# Properties

 Label 9408.bc Number of curves $4$ Conductor $9408$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bc1 9408ca3 [0, -1, 0, -29857, 1993153] [2] 24576
9408.bc2 9408ca2 [0, -1, 0, -2417, 11985] [2, 2] 12288
9408.bc3 9408ca1 [0, -1, 0, -1437, -20355] [2] 6144 $$\Gamma_0(N)$$-optimal
9408.bc4 9408ca4 [0, -1, 0, 9343, 84897] [2] 24576

## Rank

sage: E.rank()

The elliptic curves in class 9408.bc have rank $$1$$.

## Modular form9408.2.a.bc

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.