Properties

Base field 3.3.148.1
Label 3.3.148.1-25.2-a
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-a over 3.3.148.1

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

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 1\) , \( 58786385 a^{2} + 68785155 a - 27089419\) , \( 1275216929162 a^{2} + 1492114096329 a - 587634150538\bigr] \)
25.2-a2 \( \bigl[0\) , \( a + 1\) , \( a\) , \( -3046 a^{2} - 3557 a + 1402\) , \( 147974 a^{2} + 173152 a - 68191\bigr] \)
25.2-a3 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -4 a^{2} + a\) , \( 95 a^{2} - 265 a + 73\bigr] \)
25.2-a4 \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( -41518 a^{2} - 48578 a + 19134\) , \( -8607796 a^{2} - 10071865 a + 3966568\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph