# Properties

 Label 11858bk Number of curves 6 Conductor 11858 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11858.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 11858bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11858.bm5 11858bk1 [1, 1, 1, -3088, 132397] [2] 23040 $$\Gamma_0(N)$$-optimal
11858.bm4 11858bk2 [1, 1, 1, -62378, 5966533] [2] 46080
11858.bm6 11858bk3 [1, 1, 1, 26557, -2784671] [2] 69120
11858.bm3 11858bk4 [1, 1, 1, -210603, -30579823] [2] 138240
11858.bm2 11858bk5 [1, 1, 1, -1011018, -392829865] [2] 207360
11858.bm1 11858bk6 [1, 1, 1, -16189258, -25078719401] [2] 414720

## Rank

sage: E.rank()

The elliptic curves in class 11858bk have rank $$0$$.

## Modular form 11858.2.a.bm

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.