Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1764.3-h
Conductor 1764.3
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 1764.3-h over \(\Q(\sqrt{13}) \)

Isogeny class 1764.3-h contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
1764.3-h1 \( \bigl[a\) , \( -1\) , \( 1\) , \( 170 a - 682\) , \( -3495 a + 6116\bigr] \)
1764.3-h2 \( \bigl[a\) , \( -1\) , \( 1\) , \( -2\) , \( a - 2\bigr] \)
1764.3-h3 \( \bigl[a\) , \( -1\) , \( 1\) , \( -5 a + 18\) , \( -23 a + 40\bigr] \)
1764.3-h4 \( \bigl[a\) , \( -1\) , \( 1\) , \( 35 a - 142\) , \( -279 a + 488\bigr] \)
1764.3-h5 \( \bigl[a\) , \( -1\) , \( 1\) , \( 10 a - 42\) , \( 49 a - 86\bigr] \)
1764.3-h6 \( \bigl[a\) , \( -1\) , \( 1\) , \( 2730 a - 10922\) , \( -220583 a + 386020\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph