Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-181.3-a
Conductor 181.3
Rank not recorded

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Base field \(\Q(\zeta_{7})^+\)

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 181.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 181.3-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
181.3-a1 \( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( a^{2} + a - 1\) , \( 274 a^{2} - 170 a - 634\) , \( 2618 a^{2} - 1512 a - 5956\bigr] \)
181.3-a2 \( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( a^{2} + a - 1\) , \( -a^{2} + 1\) , \( -a - 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph