# Properties

 Label 139656.e Number of curves 4 Conductor 139656 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("139656.e1")

sage: E.isogeny_class()

## Elliptic curves in class 139656.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139656.e1 139656ba4 [0, -1, 0, -249864, -47983572] [2] 788480
139656.e2 139656ba2 [0, -1, 0, -17104, -593636] [2, 2] 394240
139656.e3 139656ba1 [0, -1, 0, -6524, 197748] [2] 197120 $$\Gamma_0(N)$$-optimal
139656.e4 139656ba3 [0, -1, 0, 46376, -4021556] [2] 788480

## Rank

sage: E.rank()

The elliptic curves in class 139656.e have rank $$0$$.

## Modular form 139656.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} - q^{11} + 2q^{13} + 2q^{15} - 6q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.