Properties

Base field \(\Q(\sqrt{105}) \)
Label 2.2.105.1-15.1-b
Conductor 15.1
Rank not recorded

Related objects

Learn more about

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

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

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

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

Curve label Weierstrass Coefficients
15.1-b1 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -72173 a - 333684\) , \( -45020158 a - 208149599\bigr] \)
15.1-b2 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -13 a - 54\) , \( 9992 a + 46191\bigr] \)
15.1-b3 \( \bigl[1\) , \( a + 1\) , \( a\) , \( 22947 a + 106101\) , \( -2227705 a - 10299746\bigr] \)
15.1-b4 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -6573 a - 30384\) , \( -318778 a - 1473869\bigr] \)
15.1-b5 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -3293 a - 15219\) , \( 222095 a + 1026844\bigr] \)
15.1-b6 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -88573 a - 409509\) , \( -32665003 a - 151025844\bigr] \)
15.1-b7 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -52493 a - 242694\) , \( 14698280 a + 67957129\bigr] \)
15.1-b8 \( \bigl[1\) , \( a + 1\) , \( a\) , \( -1416973 a - 6551334\) , \( -2081450248 a - 9623533989\bigr] \)

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