Properties

Base field 4.4.16317.1
Label 4.4.16317.1-25.1-c
Conductor 25.1
Rank bounds 0...1

Related objects

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Base field 4.4.16317.1

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

Elliptic curves in class 25.1-c over 4.4.16317.1

Isogeny class 25.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
25.1-c1 \( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 5 a^{3} + 5 a^{2} - 11 a - 7\) , \( -16 a^{3} + 74 a^{2} + 80 a - 172\bigr] \)
25.1-c2 \( \bigl[1\) , \( a^{3} - 5 a - 3\) , \( a + 1\) , \( -18 a^{3} - 9 a^{2} + 43 a + 8\) , \( -125 a^{3} - 98 a^{2} + 236 a + 44\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph