# Properties

 Label 7942.r Number of curves $2$ Conductor $7942$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("r1")

E.isogeny_class()

## Elliptic curves in class 7942.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.r1 7942s2 $$[1, 1, 1, -7431012, 7791144677]$$ $$7401701968633/2883584$$ $$17679444563934838784$$ $$[]$$ $$369360$$ $$2.6582$$
7942.r2 7942s1 $$[1, 1, 1, -263357, -38801645]$$ $$329474953/85184$$ $$522268748104520384$$ $$[]$$ $$123120$$ $$2.1089$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7942.r have rank $$0$$.

## Complex multiplication

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

## Modular form7942.2.a.r

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.