# Properties

 Label 1936k Number of curves $2$ Conductor $1936$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1936k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1936.b2 1936k1 [0, 1, 0, -40, 372] [] 384 $$\Gamma_0(N)$$-optimal
1936.b1 1936k2 [0, 1, 0, -58120, -5412684] [] 4224

## Rank

sage: E.rank()

The elliptic curves in class 1936k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1936k do not have complex multiplication.

## Modular form1936.2.a.k

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + 2q^{7} + q^{9} + q^{13} - 2q^{15} - 5q^{17} - 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.