Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-15.1-b
Conductor 15.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 15.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 15.1-b contains 10 curves linked by isogenies of degrees dividing 32.

Curve label Weierstrass Coefficients
15.1-b1 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2539 a - 9913\) , \( -145850 a - 565247\bigr] \)
15.1-b2 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3519 a - 13633\) , \( 412186 a + 1596397\bigr] \)
15.1-b3 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a + 7\) , \( -94 a - 363\bigr] \)
15.1-b4 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1121 a + 4347\) , \( 23958 a + 92793\bigr] \)
15.1-b5 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -319 a - 1233\) , \( 2106 a + 8157\bigr] \)
15.1-b6 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -159 a - 613\) , \( -2522 a - 9767\bigr] \)
15.1-b7 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -4319 a - 16733\) , \( 294206 a + 1139457\bigr] \)
15.1-b8 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2559 a - 9913\) , \( -144782 a - 560747\bigr] \)
15.1-b9 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -69119 a - 267833\) , \( 19314626 a + 74805717\bigr] \)
15.1-b10 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -40979 a - 158713\) , \( -8981954 a - 34786967\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 32 & 8 & 16 & 8 & 4 & 16 & 2 & 32 & 4 \\ 32 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 & 32 \\ 8 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 & 8 \\ 16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 & 16 \\ 8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 & 8 \\ 4 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 & 4 \\ 16 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 & 16 \\ 2 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 & 2 \\ 32 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 & 32 \\ 4 & 32 & 8 & 16 & 8 & 4 & 16 & 2 & 32 & 1 \end{array}\right)\)

Isogeny graph