Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-48.1-b
Conductor 48.1
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 48.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 48.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
48.1-b1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -80 a + 193\) , \( -4455 a + 10911\bigr] \)
48.1-b2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
48.1-b3 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 20 a - 52\) , \( 99 a - 244\bigr] \)
48.1-b4 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 120 a - 297\) , \( -891 a + 2181\bigr] \)
48.1-b5 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -320 a - 787\) , \( -5445 a - 13339\bigr] \)
48.1-b6 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -1920 a - 4707\) , \( 68607 a + 168051\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph