Properties

Base field 3.3.148.1
Label 3.3.148.1-475.2-b
Conductor 475.2
Rank \( 1 \)

Related objects

Learn more

Base field 3.3.148.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 3 x + 1 \); class number \(1\).

Elliptic curves in class 475.2-b over 3.3.148.1

Isogeny class 475.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
475.2-b1 \( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( a^{2} - a - 1\) , \( -114167 a^{2} - 133585 a + 52608\) , \( 38795288 a^{2} + 45393843 a - 17877301\bigr] \)
475.2-b2 \( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( a^{2} - a - 1\) , \( -274212 a^{2} - 320850 a + 126358\) , \( -90112799 a^{2} - 105439768 a + 41524980\bigr] \)
475.2-b3 \( \bigl[0\) , \( -a^{2} + a + 3\) , \( a\) , \( -25 a^{2} + 79 a - 29\) , \( 165 a^{2} - 431 a + 121\bigr] \)
475.2-b4 \( \bigl[0\) , \( -a^{2} + a + 3\) , \( a\) , \( -5 a^{2} + 9 a + 1\) , \( -6 a^{2} + 15 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph