Properties

Base field \(\Q(\sqrt{105}) \)
Label 2.2.105.1-15.1-a
Conductor 15.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 15.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 15.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
15.1-a1 \( \bigl[a\) , \( 0\) , \( 0\) , \( -68780293 a - 318003982\) , \( 1319401941438 a + 6100222396500\bigr] \)
15.1-a2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -13023 a - 60202\) , \( -294878872 a - 1363365200\bigr] \)
15.1-a3 \( \bigl[a\) , \( 0\) , \( 0\) , \( 21867472 a + 101103728\) , \( 67141172125 a + 310425556510\bigr] \)
15.1-a4 \( \bigl[a\) , \( 0\) , \( 0\) , \( -6264593 a - 28964182\) , \( 8918562808 a + 41234755600\bigr] \)
15.1-a5 \( \bigl[a\) , \( 0\) , \( 0\) , \( -3138808 a - 14512192\) , \( -6764057685 a - 31273454190\bigr] \)
15.1-a6 \( \bigl[a\) , \( 0\) , \( 0\) , \( -84409218 a - 390263932\) , \( 954779057783 a + 4414397469850\bigr] \)
15.1-a7 \( \bigl[a\) , \( 0\) , \( 0\) , \( -50025583 a - 231292042\) , \( -436078729470 a - 2016199270740\bigr] \)
15.1-a8 \( \bigl[a\) , \( 0\) , \( 0\) , \( -1350352143 a - 6243319882\) , \( 61135112671028 a + 282656688470200\bigr] \)

Rank

Rank: \( 1 \)

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