Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-144.1-f
Conductor 144.1
Rank \( 2 \)

Related objects

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Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 144.1-f over \(\Q(\sqrt{14}) \)

Isogeny class 144.1-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
144.1-f1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -467 a + 1770\) , \( -78662 a + 294347\bigr] \)
144.1-f2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
144.1-f3 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 133 a - 475\) , \( 1201 a - 4473\bigr] \)
144.1-f4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -733 a - 2720\) , \( 19624 a + 73447\bigr] \)
144.1-f5 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1933 a - 7210\) , \( 89758 a - 335823\bigr] \)
144.1-f6 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 11533 a - 43130\) , \( -1300666 a + 4866667\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph