Properties

Base field 3.3.148.1
Label 3.3.148.1-25.2-b
Conductor 25.2
Rank \( 0 \)

Related objects

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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 25.2-b over 3.3.148.1

Isogeny class 25.2-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
25.2-b1 \( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 1\) , \( 10713 a^{2} + 12536 a - 4937\) , \( 3135860 a^{2} + 3669228 a - 1445040\bigr] \)
25.2-b2 \( \bigl[0\) , \( a^{2} - 2 a - 3\) , \( 1\) , \( -377381 a^{2} - 441567 a + 173905\) , \( -232144315 a^{2} - 271628927 a + 106974682\bigr] \)
25.2-b3 \( \bigl[0\) , \( -a^{2} + 2 a + 2\) , \( a\) , \( -a^{2} - a + 4\) , \( -a^{2} + a + 2\bigr] \)
25.2-b4 \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - 2\) , \( -5312850765 a^{2} - 6216494888 a + 2448220752\) , \( -394174470602711 a^{2} - 461218221425205 a + 181639982107606\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph