Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-144.5-c
Conductor 144.5
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 144.5-c over \(\Q(\sqrt{17}) \)

Isogeny class 144.5-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
144.5-c1 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -119 a - 186\) , \( -1469 a - 2294\bigr] \)
144.5-c2 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 206 a - 531\) , \( -2387 a + 6120\bigr] \)
144.5-c3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 142 a + 223\) , \( -1372 a - 2142\bigr] \)
144.5-c4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -53 a - 82\) , \( -221 a - 345\bigr] \)
144.5-c5 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 11 a - 36\) , \( -41 a + 102\bigr] \)
144.5-c6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 11\) , \( -15 a - 26\bigr] \)
144.5-c7 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -117 a - 183\) , \( 876 a + 1368\bigr] \)
144.5-c8 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -78 a - 116\) , \( -639 a - 1034\bigr] \)

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