Properties

 Label 130.a Number of curves 4 Conductor 130 CM no Rank 1 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("130.a1")
sage: E.isogeny_class()

Elliptic curves in class 130.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
130.a1 130a3 [1, 0, 1, -208, -1122] 2 72
130.a2 130a1 [1, 0, 1, -33, 68] 6 24 $$\Gamma_0(N)$$-optimal
130.a3 130a2 [1, 0, 1, -13, 156] 6 48
130.a4 130a4 [1, 0, 1, 112, -4194] 2 144

Rank

sage: E.rank()

The elliptic curves in class 130.a have rank $$1$$.

Modular form130.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} - 6q^{11} - 2q^{12} + q^{13} + 4q^{14} - 2q^{15} + q^{16} - 6q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 