# Properties

 Label 39326.m Number of curves 6 Conductor 39326 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39326.m1")

sage: E.isogeny_class()

## Elliptic curves in class 39326.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39326.m1 39326l6 [1, 1, 1, -7670033, -8179253777] [2] 898560
39326.m2 39326l5 [1, 1, 1, -478993, -128165393] [2] 449280
39326.m3 39326l4 [1, 1, 1, -99778, -9985145] [2] 299520
39326.m4 39326l2 [1, 1, 1, -29553, 1941869] [2] 99840
39326.m5 39326l1 [1, 1, 1, -1463, 42985] [2] 49920 $$\Gamma_0(N)$$-optimal
39326.m6 39326l3 [1, 1, 1, 12582, -906457] [2] 149760

## Rank

sage: E.rank()

The elliptic curves in class 39326.m have rank $$1$$.

## Modular form 39326.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{7} + q^{8} + q^{9} + 2q^{12} - 4q^{13} + q^{14} + q^{16} + 6q^{17} + q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.