Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-8.1-d
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-d over \(\Q(\sqrt{15}) \)

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

Curve label Weierstrass Coefficients
8.1-d1 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -4\) , \( -2\bigr] \)
8.1-d2 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 49\) , \( -36 a + 125\bigr] \)
8.1-d3 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9\) , \( -2 a - 7\bigr] \)
8.1-d4 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -10 a - 49\) , \( -56 a - 219\bigr] \)

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