Properties

Base field 5.5.65657.1
Label 5.5.65657.1-25.1-c
Conductor 25.1
Rank not recorded

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Base field 5.5.65657.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 25.1-c over 5.5.65657.1

Isogeny class 25.1-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
25.1-c1 \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{3} - 4 a - 1\) , \( 1015 a^{4} - 1849 a^{3} - 3633 a^{2} + 4940 a + 991\) , \( -23261 a^{4} + 41576 a^{3} + 81774 a^{2} - 113086 a - 22399\bigr] \)
25.1-c2 \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -125 a^{4} + 373 a^{3} + 183 a^{2} - 759 a - 265\) , \( 241 a^{4} - 2229 a^{3} + 3233 a^{2} + 1399 a + 390\bigr] \)
25.1-c3 \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 3\) , \( a\) , \( -6 a^{4} + 5 a^{3} + 21 a^{2} - 20 a - 6\) , \( 148 a^{4} + 191 a^{3} - 275 a^{2} - 325 a - 59\bigr] \)
25.1-c4 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 10 a - 10\) , \( a^{2} - a - 2\) , \( 4 a^{4} - 3 a^{3} - 20 a^{2} + 5 a + 15\) , \( -11 a^{4} + 49 a^{2} + 27 a - 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph