# Properties

 Label 7406.e Number of curves $2$ Conductor $7406$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 7406.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.e1 7406c2 $$[1, 1, 0, -320320, -65460864]$$ $$24553362849625/1755162752$$ $$259827078332006528$$ $$[2]$$ $$118272$$ $$2.0885$$
7406.e2 7406c1 $$[1, 1, 0, 18240, -4452352]$$ $$4533086375/60669952$$ $$-8981330279907328$$ $$[2]$$ $$59136$$ $$1.7419$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7406.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7406.e do not have complex multiplication.

## Modular form7406.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 4 q^{11} + 2 q^{12} + q^{14} + q^{16} - 6 q^{17} - q^{18} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.