Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-104.3-b
Conductor 104.3
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 104.3-b over \(\Q(\zeta_{7})^+\)

Isogeny class 104.3-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
104.3-b1 \( \bigl[a\) , \( -a + 1\) , \( a^{2} - 1\) , \( -1130 a^{2} + 558 a - 29\) , \( -22648 a^{2} + 11295 a - 549\bigr] \)
104.3-b2 \( \bigl[a\) , \( -a + 1\) , \( a^{2} - 1\) , \( -5 a^{2} + 13 a - 4\) , \( -74 a^{2} - 5 a + 17\bigr] \)
104.3-b3 \( \bigl[a\) , \( -a + 1\) , \( a^{2} - 1\) , \( -2 a + 1\) , \( 2 a^{2} + a - 1\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph