Properties

 Label 15162l Number of curves $6$ Conductor $15162$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("15162.j1")

sage: E.isogeny_class()

Elliptic curves in class 15162l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15162.j5 15162l1 [1, 0, 1, -1452, -47126] [2] 27648 $$\Gamma_0(N)$$-optimal
15162.j4 15162l2 [1, 0, 1, -30332, -2034070] [2, 2] 55296
15162.j1 15162l3 [1, 0, 1, -485192, -130122646] [2] 110592
15162.j3 15162l4 [1, 0, 1, -37552, -994390] [2, 2] 110592
15162.j2 15162l5 [1, 0, 1, -329962, 72225074] [2] 221184
15162.j6 15162l6 [1, 0, 1, 139338, -7645454] [2] 221184

Rank

sage: E.rank()

The elliptic curves in class 15162l have rank $$1$$.

Modular form 15162.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} + q^{14} - 2q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.