Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-113.1-a
Conductor 113.1
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 113.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 113.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
113.1-a1 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 175 a^{2} - 99 a - 400\) , \( 1306 a^{2} - 733 a - 2948\bigr] \)
113.1-a2 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 5 a^{2} + 11 a - 50\) , \( -54 a^{2} + 85 a + 28\bigr] \)
113.1-a3 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 10 a^{2} - 4 a - 25\) , \( 16 a^{2} - 8 a - 38\bigr] \)
113.1-a4 \( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( a\) , \( a^{2} - 2\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph