Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-41.2-a
Conductor 41.2
Rank not recorded

Related objects

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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 41.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 41.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
41.2-a1 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a^{2} - 89 a - 140\) , \( -216 a^{2} - 736 a - 678\bigr] \)
41.2-a2 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( 4 a^{2} - 6 a + 2\bigr] \)
41.2-a3 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \)
41.2-a4 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -75 a^{2} - 69 a + 35\) , \( -646 a^{2} - 526 a + 340\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph