Properties

Base field 4.4.6125.1
Label 4.4.6125.1-25.1-c
Conductor 25.1
Rank \( 0 \)

Related objects

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Base field 4.4.6125.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 9 x^{2} + 9 x + 11 \); class number \(1\).

Elliptic curves in class 25.1-c over 4.4.6125.1

Isogeny class 25.1-c contains 4 curves linked by isogenies of degrees dividing 35.

Curve label Weierstrass Coefficients
25.1-c1 \( \bigl[0\) , \( 2 a^{3} + 3 a^{2} - 13 a - 11\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -15 a^{3} + 2 a^{2} + 103 a - 56\) , \( 45 a^{3} - 32 a^{2} - 326 a + 353\bigr] \)
25.1-c2 \( \bigl[0\) , \( a^{3} + 2 a^{2} - 6 a - 9\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( 50 a^{3} + 66 a^{2} - 287 a - 225\) , \( 174 a^{3} + 235 a^{2} - 1000 a - 809\bigr] \)
25.1-c3 \( \bigl[0\) , \( a - 1\) , \( a\) , \( -60 a^{3} - 73 a^{2} + 376 a + 297\) , \( -201 a^{3} - 245 a^{2} + 1267 a + 998\bigr] \)
25.1-c4 \( \bigl[0\) , \( -a^{3} - 2 a^{2} + 5 a + 9\) , \( a\) , \( 62 a^{3} + 75 a^{2} - 389 a - 299\) , \( -255 a^{3} - 311 a^{2} + 1607 a + 1270\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 35 & 7 \\ 5 & 1 & 7 & 35 \\ 35 & 7 & 1 & 5 \\ 7 & 35 & 5 & 1 \end{array}\right)\)

Isogeny graph