Properties

 Label 363726.j Number of curves 2 Conductor 363726 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("363726.j1")
sage: E.isogeny_class()

Elliptic curves in class 363726.j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
363726.j1 363726j2 [1, -1, 0, -135603, -19133955] 2 2949120 $$\Gamma_0(N)$$-optimal*
363726.j2 363726j1 [1, -1, 0, -4923, -551259] 2 1474560 $$\Gamma_0(N)$$-optimal*
*optimality has not been proved rigorously for conductors over 270000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 363726.j2.

Rank

sage: E.rank()

The elliptic curves in class 363726.j have rank $$0$$.

Modular form None

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - 2q^{5} + 4q^{7} - q^{8} + 2q^{10} - 4q^{14} + q^{16} - 4q^{17} + 4q^{19} + O(q^{20})$$

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.