Properties

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

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

Curve label Weierstrass Coefficients
10.1-g1 \( \bigl[1\) , \( -a\) , \( 0\) , \( -404 a + 1569\) , \( -14780 a + 57241\bigr] \)
10.1-g2 \( \bigl[1\) , \( -a\) , \( 0\) , \( 186 a - 716\) , \( -2474 a + 9580\bigr] \)
10.1-g3 \( \bigl[1\) , \( -a\) , \( 0\) , \( 2981 a - 11541\) , \( -170271 a + 659455\bigr] \)
10.1-g4 \( \bigl[1\) , \( -a\) , \( 0\) , \( 3146 a - 12181\) , \( -149650 a + 579591\bigr] \)

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