Properties

 Label 38.b Number of curves 2 Conductor 38 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38.b1")
sage: E.isogeny_class()

Elliptic curves in class 38.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
38.b1 38b2 [1, 1, 1, -70, -279] 1 10
38.b2 38b1 [1, 1, 1, 0, 1] 5 2 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 38.b have rank $$0$$.

Modular form38.2.a.b

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

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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 