Properties

Base field \(\Q(\sqrt{105}) \)
Label 2.2.105.1-21.1-a
Conductor 21.1
Rank not recorded

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Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 21.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 21.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
21.1-a1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3167 a - 14627\) , \( 613514 a + 2836587\bigr] \)
21.1-a2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 88 a + 423\) , \( 272 a + 1279\bigr] \)
21.1-a3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -377 a - 1727\) , \( 1748 a + 8103\bigr] \)
21.1-a4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3632 a - 16777\) , \( -269278 a - 1244981\bigr] \)
21.1-a5 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4562 a - 21077\) , \( 376778 a + 1742043\bigr] \)
21.1-a6 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -72917 a - 337127\) , \( 24227822 a + 112016739\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph