Properties

Base field 4.4.19225.1
Label 4.4.19225.1-9.2-a
Conductor 9.2
Rank bounds 0...1

Related objects

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Base field 4.4.19225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 15 x^{2} + 2 x + 44 \); class number \(1\).

Elliptic curves in class 9.2-a over 4.4.19225.1

Isogeny class 9.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
9.2-a1 \( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{7}{2} a - 7\) , \( -a^{3} + 4 a^{2} + 7 a - 22\) , \( 3 a^{3} - 13 a^{2} - 15 a + 68\) , \( 13 a^{3} - 48 a^{2} - 77 a + 241\bigr] \)
9.2-a2 \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 7\) , \( 1\) , \( \frac{65}{2} a^{3} + \frac{81}{2} a^{2} - \frac{899}{2} a - 864\) , \( \frac{971}{2} a^{3} + \frac{913}{2} a^{2} - \frac{12981}{2} a - 11486\bigr] \)

Rank

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

Isogeny matrix

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

Isogeny graph