Properties

Base field 4.4.18625.1
Label 4.4.18625.1-11.1-a
Conductor 11.1
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Base field 4.4.18625.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 9 x + 41 \); class number \(1\).

Elliptic curves in class 11.1-a over 4.4.18625.1

Isogeny class 11.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
11.1-a1 \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{59}{3} a^{3} + 85 a^{2} - \frac{544}{3} a - \frac{2368}{3}\) , \( \frac{917}{3} a^{3} + 78 a^{2} - \frac{8992}{3} a - \frac{3031}{3}\bigr] \)
11.1-a2 \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( a + 1\) , \( \frac{47}{6} a^{3} + 17 a^{2} - \frac{155}{3} a - \frac{547}{6}\) , \( \frac{611}{3} a^{3} + 320 a^{2} - \frac{6034}{3} a - \frac{9808}{3}\bigr] \)
11.1-a3 \( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( 0\) , \( -\frac{8}{3} a^{3} + 5 a^{2} + \frac{100}{3} a - \frac{200}{3}\) , \( \frac{27}{2} a^{3} - 33 a^{2} - 148 a + \frac{731}{2}\bigr] \)
11.1-a4 \( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( 0\) , \( -\frac{1}{6} a^{3} + \frac{10}{3} a + \frac{5}{6}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{8}{3} a + \frac{31}{3}\bigr] \)

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Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph