Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-36.3-a
Conductor 36.3
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 36.3-a over \(\Q(\sqrt{13}) \)

Isogeny class 36.3-a contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
36.3-a1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -85 a + 94\) , \( -352 a + 209\bigr] \)
36.3-a2 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
36.3-a3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -124 a - 173\) , \( -1087 a - 1405\bigr] \)
36.3-a4 \( \bigl[1\) , \( -a\) , \( a\) , \( -4 a - 4\) , \( -15 a - 20\bigr] \)
36.3-a5 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a + 2\) , \( 3 a + 4\bigr] \)
36.3-a6 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 114 a - 191\) , \( -670 a + 1528\bigr] \)

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