Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-10.1-e
Conductor 10.1
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 10.1-e over \(\Q(\sqrt{15}) \)

Isogeny class 10.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
10.1-e1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 52 a - 200\) , \( -1640 a + 6352\bigr] \)
10.1-e2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7452 a - 28860\) , \( -674560 a + 2612560\bigr] \)
10.1-e3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 119252 a - 461860\) , \( -43879600 a + 169944960\bigr] \)
10.1-e4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1472 a - 5700\) , \( -57504 a + 222712\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph