Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-23.5-a
Conductor 23.5
Rank not recorded

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Base field \(\Q(\zeta_{11})^+\)

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1 \); class number \(1\).

Elliptic curves in class 23.5-a over \(\Q(\zeta_{11})^+\)

Isogeny class 23.5-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
23.5-a1 \( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{4} + 3 a^{2} + a + 1\) , \( a\) , \( -308 a^{4} + 310 a^{3} + 1145 a^{2} - 661 a - 1021\) , \( -4125 a^{4} + 3861 a^{3} + 15898 a^{2} - 8465 a - 13846\bigr] \)
23.5-a2 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 5 a + 6\) , \( -a^{2} - a + 3\bigr] \)
23.5-a3 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 12 a^{4} - 18 a^{3} - 37 a^{2} + 45 a + 6\) , \( -18 a^{4} + 26 a^{3} + 47 a^{2} - 72 a + 15\bigr] \)
23.5-a4 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 247 a^{4} - 703 a^{3} - 792 a^{2} + 1375 a - 829\) , \( 3387 a^{4} - 14884 a^{3} - 12485 a^{2} + 30720 a - 11294\bigr] \)

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