Properties

Base field \(\Q(\sqrt{34}) \)
Label 2.2.136.1-18.1-f
Conductor 18.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{34}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 34 \); class number \(2\).

Elliptic curves in class 18.1-f over \(\Q(\sqrt{34}) \)

Isogeny class 18.1-f contains 8 curves linked by isogenies of degrees dividing 20.

Curve label Weierstrass Coefficients
18.1-f1 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -307 a - 6346\) , \( -15106 a - 223719\bigr] \)
18.1-f2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2088 a + 7104\) , \( 1636360 a + 9432569\bigr] \)
18.1-f3 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -12662 a - 73136\) , \( -1237372 a - 7090263\bigr] \)
18.1-f4 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -47 a - 266\) , \( -442 a - 2631\bigr] \)
18.1-f5 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4967 a - 31016\) , \( 459902 a + 2709765\bigr] \)
18.1-f6 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -687 a - 4266\) , \( -25658 a - 152455\bigr] \)
18.1-f7 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4927 a - 30766\) , \( 468086 a + 2758161\bigr] \)
18.1-f8 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11307 a - 66186\) , \( -1602674 a - 9348007\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\ 5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\ 20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\ 4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\ 10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\ 2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\ 20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\ 4 & 20 & 5 & 4 & 10 & 2 & 20 & 1 \end{array}\right)\)

Isogeny graph