# Properties

 Label 4032.m Number of curves $6$ Conductor $4032$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4032.m1")

sage: E.isogeny_class()

## Elliptic curves in class 4032.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.m1 4032bl4 [0, 0, 0, -774156, 262174736] [2] 24576
4032.m2 4032bl5 [0, 0, 0, -526476, -145621744] [2] 49152
4032.m3 4032bl3 [0, 0, 0, -59916, 1997840] [2, 2] 24576
4032.m4 4032bl2 [0, 0, 0, -48396, 4094480] [2, 2] 12288
4032.m5 4032bl1 [0, 0, 0, -2316, 94736] [2] 6144 $$\Gamma_0(N)$$-optimal
4032.m6 4032bl6 [0, 0, 0, 222324, 15432464] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 4032.m have rank $$0$$.

## Modular form4032.2.a.m

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} + 4q^{11} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.