Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1156.2-b
Conductor 1156.2
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 1156.2-b over \(\Q(\sqrt{13}) \)

Isogeny class 1156.2-b contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
1156.2-b1 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -555 a + 811\) , \( -2520 a + 9274\bigr] \)
1156.2-b2 \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -11 a - 16\) , \( -39 a - 44\bigr] \)
1156.2-b3 \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -521 a - 767\) , \( 9127 a + 12156\bigr] \)
1156.2-b4 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -16 a - 21\) , \( 159 a + 205\bigr] \)
1156.2-b5 \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 4 a + 8\) , \( -23 a - 30\bigr] \)
1156.2-b6 \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 784 a - 1526\) , \( -13814 a + 33114\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 45 & 3 & 5 & 15 & 9 \\ 45 & 1 & 15 & 9 & 3 & 5 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 5 & 9 & 15 & 1 & 3 & 45 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 5 & 3 & 45 & 15 & 1 \end{array}\right)\)

Isogeny graph