# Properties

 Label 7942.k Number of curves $2$ Conductor $7942$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 7942.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.k1 7942c2 $$[1, 1, 0, -41743159, -29278902123]$$ $$24928563670864867/13279961395712$$ $$4285280169376300882523648$$ $$[2]$$ $$1504800$$ $$3.4178$$
7942.k2 7942c1 $$[1, 1, 0, -24184119, 45420765845]$$ $$4847659921191907/42218553344$$ $$13623407782135261822976$$ $$[2]$$ $$752400$$ $$3.0712$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7942.k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7942.k do not have complex multiplication.

## Modular form7942.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{14} + 4 q^{15} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})$$

## 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.