# Properties

 Label 32487.e Number of curves $6$ Conductor $32487$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 32487.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.e1 32487m6 $$[1, 0, 0, -1988372, 1078244103]$$ $$7389727131216686257/6115533215337$$ $$719486367251182713$$ $$[2]$$ $$589824$$ $$2.3548$$
32487.e2 32487m4 $$[1, 0, 0, -151607, 8879520]$$ $$3275619238041697/1605271262049$$ $$188858558708802801$$ $$[2, 2]$$ $$294912$$ $$2.0083$$
32487.e3 32487m2 $$[1, 0, 0, -80802, -8750925]$$ $$495909170514577/6224736609$$ $$732334037312241$$ $$[2, 2]$$ $$147456$$ $$1.6617$$
32487.e4 32487m1 $$[1, 0, 0, -80557, -8807128]$$ $$491411892194497/78897$$ $$9282153153$$ $$[2]$$ $$73728$$ $$1.3151$$ $$\Gamma_0(N)$$-optimal
32487.e5 32487m3 $$[1, 0, 0, -13917, -22783398]$$ $$-2533811507137/1904381781393$$ $$-224048612199105057$$ $$[2]$$ $$294912$$ $$2.0083$$
32487.e6 32487m5 $$[1, 0, 0, 552278, 68146637]$$ $$158346567380527343/108665074944153$$ $$-12784337402104656297$$ $$[2]$$ $$589824$$ $$2.3548$$

## Rank

sage: E.rank()

The elliptic curves in class 32487.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32487.e do not have complex multiplication.

## Modular form 32487.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - q^{12} - q^{13} + 2 q^{15} - q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.