# 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 structure Modular degree Optimality
363726.j1 363726j2 [1, -1, 0, -135603, -19133955]  2949120
363726.j2 363726j1 [1, -1, 0, -4923, -551259]  1474560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 363726.2.a.j

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. 