Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-15.1-d
Conductor 15.1
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 15.1-d over \(\Q(\sqrt{15}) \)

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

Curve label Weierstrass Coefficients
15.1-d1 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2543 a - 9924\) , \( 138228 a + 535486\bigr] \)
15.1-d2 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3523 a - 13644\) , \( -422748 a - 1637318\bigr] \)
15.1-d3 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 4\) , \( 92 a + 362\bigr] \)
15.1-d4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1117 a + 4336\) , \( -20600 a - 79774\bigr] \)
15.1-d5 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -323 a - 1244\) , \( -3068 a - 11878\bigr] \)
15.1-d6 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -163 a - 624\) , \( 2040 a + 7906\bigr] \)
15.1-d7 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -4323 a - 16744\) , \( -307168 a - 1189678\bigr] \)
15.1-d8 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2563 a - 9924\) , \( 137100 a + 530986\bigr] \)
15.1-d9 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -69123 a - 267844\) , \( -19521988 a - 75609238\bigr] \)
15.1-d10 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -40983 a - 158724\) , \( 8859012 a + 34310806\bigr] \)

Rank

Rank not yet determined.

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