# Properties

 Label 726.i Number of curves $4$ Conductor $726$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 726.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
726.i1 726h3 $$[1, 0, 0, -9743, 367929]$$ $$57736239625/255552$$ $$452725956672$$ $$[2]$$ $$1440$$ $$1.0889$$
726.i2 726h4 $$[1, 0, 0, -4903, 734801]$$ $$-7357983625/127552392$$ $$-225966843123912$$ $$[2]$$ $$2880$$ $$1.4354$$
726.i3 726h1 $$[1, 0, 0, -668, -6324]$$ $$18609625/1188$$ $$2104614468$$ $$[2]$$ $$480$$ $$0.53956$$ $$\Gamma_0(N)$$-optimal
726.i4 726h2 $$[1, 0, 0, 542, -26410]$$ $$9938375/176418$$ $$-312535248498$$ $$[2]$$ $$960$$ $$0.88614$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 726.i do not have complex multiplication.

## Modular form726.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.