Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1872.1-h
Conductor 1872.1
Rank \( 1 \)

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 1872.1-h over \(\Q(\sqrt{13}) \)

Isogeny class 1872.1-h contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
1872.1-h1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 3055 a - 7753\) , \( 134485 a - 317899\bigr] \)
1872.1-h2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 55 a - 73\) , \( 205 a - 451\bigr] \)
1872.1-h3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( -4\bigr] \)
1872.1-h4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -748\) , \( -7564\bigr] \)
1872.1-h5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -55 a - 18\) , \( -205 a - 246\bigr] \)
1872.1-h6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -148\) , \( 644\bigr] \)
1872.1-h7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -733\) , \( -7888\bigr] \)
1872.1-h8 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3055 a - 4698\) , \( -134485 a - 183414\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph