Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1521.1-h
Conductor 1521.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 1521.1-h over \(\Q(\sqrt{13}) \)

Isogeny class 1521.1-h contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
1521.1-h1 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11 a - 13\) , \( -55 a - 71\bigr] \)
1521.1-h2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 1312 a - 3083\) , \( -33562 a + 77613\bigr] \)
1521.1-h3 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 899 a + 52\) , \( -14940 a - 5427\bigr] \)
1521.1-h4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 12 a - 28\) , \( 43 a - 101\bigr] \)
1521.1-h5 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -163 a - 218\) , \( 828 a + 1070\bigr] \)
1521.1-h6 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -206 a - 338\) , \( -2135 a - 2580\bigr] \)
1521.1-h7 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1311 a - 1768\) , \( 32250 a + 42283\bigr] \)
1521.1-h8 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1138 a - 1583\) , \( -28812 a - 37969\bigr] \)
1521.1-h9 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 207 a - 548\) , \( 1928 a - 4170\bigr] \)
1521.1-h10 \( \bigl[1\) , \( 1\) , \( a\) , \( 162 a - 380\) , \( -829 a + 1899\bigr] \)
1521.1-h11 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -898 a + 947\) , \( 15838 a - 21317\bigr] \)
1521.1-h12 \( \bigl[1\) , \( 1\) , \( a\) , \( 1137 a - 2720\) , \( 28811 a - 66780\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 4 & 8 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 6 & 12 & 8 & 2 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 2 & 4 & 24 & 6 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 12 & 24 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 6 & 12 & 2 & 2 & 3 & 4 & 6 \\ 4 & 6 & 2 & 12 & 6 & 1 & 2 & 12 & 3 & 2 & 6 & 4 \\ 8 & 12 & 4 & 24 & 12 & 2 & 1 & 24 & 6 & 4 & 3 & 8 \\ 12 & 8 & 24 & 4 & 2 & 12 & 24 & 1 & 4 & 6 & 8 & 3 \\ 12 & 2 & 6 & 4 & 2 & 3 & 6 & 4 & 1 & 6 & 2 & 12 \\ 2 & 12 & 4 & 6 & 3 & 2 & 4 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 6 & 3 & 8 & 2 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 4 & 8 & 3 & 12 & 2 & 24 & 1 \end{array}\right)\)

Isogeny graph