Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-104.1-a
Conductor 104.1
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 104.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 104.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
104.1-a1 \( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2\) , \( -40 a^{2} - 10 a\) , \( -150 a^{2} - 66 a + 6\bigr] \)
104.1-a2 \( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2\) , \( 0\) , \( 0\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph