Properties

 Label 147a Number of curves 6 Conductor 147 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("147.a1")

sage: E.isogeny_class()

Elliptic curves in class 147a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
147.a6 147a1 [1, 1, 1, 48, 48] [4] 24 $$\Gamma_0(N)$$-optimal
147.a5 147a2 [1, 1, 1, -197, 146] [2, 2] 48
147.a3 147a3 [1, 1, 1, -1912, -32782] [2] 96
147.a2 147a4 [1, 1, 1, -2402, 44246] [2, 2] 96
147.a1 147a5 [1, 1, 1, -38417, 2882228] [2] 192
147.a4 147a6 [1, 1, 1, -1667, 72764] [2] 192

Rank

sage: E.rank()

The elliptic curves in class 147a have rank $$0$$.

Modular form147.2.a.a

sage: E.q_eigenform(10)

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

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 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.