Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-8.1-b
Conductor 8.1
Rank not recorded

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 8.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 8.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
8.1-b1 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -125 a - 476\) , \( 3263 a + 12642\bigr] \)
8.1-b2 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3235 a - 12521\) , \( 67026 a + 259595\bigr] \)
8.1-b3 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2605 a - 10081\) , \( 141300 a + 547257\bigr] \)
8.1-b4 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -41655 a - 161321\) , \( 9092142 a + 35213719\bigr] \)

Rank

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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