Properties

Base field \(\Q(\sqrt{205}) \)
Label 2.2.205.1-45.1-b
Conductor 45.1
Rank not recorded

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Base field \(\Q(\sqrt{205}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 51 \); class number \(2\).

Elliptic curves in class 45.1-b over \(\Q(\sqrt{205}) \)

Isogeny class 45.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
45.1-b1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -18393723 a - 122482233\) , \( -215718071184 a - 1436447336562\bigr] \)
45.1-b2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -891648 a - 5937408\) , \( 197425299456 a + 1314637406208\bigr] \)
45.1-b3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 5847957 a + 38941047\) , \( -10966442256 a - 73024557858\bigr] \)
45.1-b4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1675323 a - 11155833\) , \( -1460655504 a - 9726374322\bigr] \)
45.1-b5 \( \bigl[0\) , \( 0\) , \( 0\) , \( 13430448 a - 102862656\) , \( -70681476096 a + 541343101824\bigr] \)
45.1-b6 \( \bigl[0\) , \( 0\) , \( 0\) , \( 22573323 a - 172887156\) , \( 156118297104 a - 1195696070226\bigr] \)
45.1-b7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -214051248 a - 1425349008\) , \( 4561034075136 a + 30371517848448\bigr] \)
45.1-b8 \( \bigl[0\) , \( 0\) , \( 0\) , \( -361120923 a - 2404673433\) , \( -9994607585424 a - 66553197732882\bigr] \)

Rank

Rank not yet determined.

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