Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-144.4-c
Conductor 144.4
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 144.4-c over \(\Q(\sqrt{17}) \)

Isogeny class 144.4-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
144.4-c1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 117 a - 300\) , \( -876 a + 2244\bigr] \)
144.4-c2 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 80 a - 192\) , \( 523 a - 1360\bigr] \)
144.4-c3 \( \bigl[a\) , \( 0\) , \( 0\) , \( -142 a + 365\) , \( 1372 a - 3514\bigr] \)
144.4-c4 \( \bigl[a\) , \( 0\) , \( 0\) , \( 53 a - 135\) , \( 221 a - 566\bigr] \)
144.4-c5 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 5 a - 12\) , \( 4 a - 28\bigr] \)
144.4-c6 \( \bigl[a\) , \( -a\) , \( a\) , \( -13 a - 23\) , \( 40 a + 62\bigr] \)
144.4-c7 \( \bigl[a\) , \( -a\) , \( a\) , \( 117 a - 303\) , \( 1468 a - 3762\bigr] \)
144.4-c8 \( \bigl[a\) , \( -a\) , \( a\) , \( -208 a - 323\) , \( 2386 a + 3734\bigr] \)

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