# Properties

 Label 726.i Number of curves 4 Conductor 726 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("726.i1")

sage: E.isogeny_class()

## Elliptic curves in class 726.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
726.i1 726h3 [1, 0, 0, -9743, 367929]  1440
726.i2 726h4 [1, 0, 0, -4903, 734801]  2880
726.i3 726h1 [1, 0, 0, -668, -6324]  480 $$\Gamma_0(N)$$-optimal
726.i4 726h2 [1, 0, 0, 542, -26410]  960

## Rank

sage: E.rank()

The elliptic curves in class 726.i have rank $$0$$.

## Modular form726.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{12} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 