# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.m1")
sage: E.isogeny_class()

## Elliptic curves in class 9408cd

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9408.m6 9408cd1 [0, -1, 0, 3071, -15455] 2 12288 $$\Gamma_0(N)$$-optimal
9408.m5 9408cd2 [0, -1, 0, -12609, -112671] 4 24576
9408.m2 9408cd3 [0, -1, 0, -153729, -23115231] 4 49152
9408.m3 9408cd4 [0, -1, 0, -122369, 16417185] 2 49152
9408.m1 9408cd5 [0, -1, 0, -2458689, -1483076895] 2 98304
9408.m4 9408cd6 [0, -1, 0, -106689, -37575327] 2 98304

## Rank

sage: E.rank()

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

## Modular form9408.2.a.m

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.