Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-441.1-a
Conductor 441.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 441.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 441.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
441.1-a1 \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 11430 a - 30242\) , \( -3021358 a + 7993761\bigr] \)
441.1-a2 \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4956 a - 13127\) , \( 2950874 a + 7807239\bigr] \)
441.1-a3 \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -330 a + 873\) , \( -1537 a + 4066\bigr] \)
441.1-a4 \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -1351 a - 3572\) , \( -7900 a - 20903\bigr] \)
441.1-a5 \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -13111 a - 34687\) , \( 1336023 a + 3534782\bigr] \)
441.1-a6 \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 16470 a - 43577\) , \( -1850335 a + 4895526\bigr] \)
441.1-a7 \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 4955 a - 13127\) , \( 2950874 a - 7807241\bigr] \)
441.1-a8 \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 263430 a - 696992\) , \( -119416672 a + 315946791\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph