# Properties

 Label 139650.en Number of curves $2$ Conductor $139650$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("en1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.en

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.en1 139650dr1 $$[1, 1, 1, -8683438, -9852240469]$$ $$114840864304543/3119040$$ $$1966633037145000000$$ $$[2]$$ $$6193152$$ $$2.6142$$ $$\Gamma_0(N)$$-optimal
139650.en2 139650dr2 $$[1, 1, 1, -8340438, -10665836469]$$ $$-101762531964703/19000801800$$ $$-11980482633157696875000$$ $$[2]$$ $$12386304$$ $$2.9608$$

## Rank

sage: E.rank()

The elliptic curves in class 139650.en have rank $$1$$.

## Complex multiplication

The elliptic curves in class 139650.en do not have complex multiplication.

## Modular form 139650.2.a.en

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - 6 q^{11} - q^{12} + 2 q^{13} + q^{16} - 4 q^{17} + q^{18} - q^{19} + O(q^{20})$$

## 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.