# Properties

 Label 9408bj Number of curves 6 Conductor 9408 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9408.bv1")
sage: E.isogeny_class()

## Elliptic curves in class 9408bj

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9408.bv6 9408bj1 [0, 1, 0, 3071, 15455] 2 12288 $$\Gamma_0(N)$$-optimal
9408.bv5 9408bj2 [0, 1, 0, -12609, 112671] 4 24576
9408.bv3 9408bj3 [0, 1, 0, -122369, -16417185] 2 49152
9408.bv2 9408bj4 [0, 1, 0, -153729, 23115231] 4 49152
9408.bv1 9408bj5 [0, 1, 0, -2458689, 1483076895] 2 98304
9408.bv4 9408bj6 [0, 1, 0, -106689, 37575327] 2 98304

## Rank

sage: E.rank()

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

## Modular form9408.2.a.bv

sage: E.q_eigenform(10)
$$q + q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.