Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-15.2-b
Conductor 15.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{21}) \)

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

Elliptic curves in class 15.2-b over \(\Q(\sqrt{21}) \)

Isogeny class 15.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
15.2-b1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 5 a - 90\) , \( 8 a - 403\bigr] \)
15.2-b2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
15.2-b3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 55\) , \( -57 a + 152\bigr] \)
15.2-b4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -3 a - 3\bigr] \)
15.2-b5 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a - 35\) , \( -81 a - 150\bigr] \)
15.2-b6 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -275 a - 460\) , \( -4022 a - 7205\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph