Properties

 Label 9537j Number of curves 4 Conductor 9537 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9537.m1")

sage: E.isogeny_class()

Elliptic curves in class 9537j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9537.m3 9537j1 [1, 0, 1, -1885, -31381] [2] 7680 $$\Gamma_0(N)$$-optimal
9537.m2 9537j2 [1, 0, 1, -3330, 22951] [2, 2] 15360
9537.m1 9537j3 [1, 0, 1, -42345, 3347029] [2] 30720
9537.m4 9537j4 [1, 0, 1, 12565, 181901] [2] 30720

Rank

sage: E.rank()

The elliptic curves in class 9537j have rank $$0$$.

Modular form9537.2.a.m

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.