Elliptic curve isogeny class 11.2-a over number field 4.4.11525.1

• Base field: 4.4.11525.1
• Label: 4.4.11525.1-11.2-a
• Conductor: 11.2
• Rank: \( 0 \)

Base field 4.4.11525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 5 x + 25 \); class number \(1\).

Elliptic curves in class 11.2-a over 4.4.11525.1

Isogeny class 11.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
11.2-a1	\( \bigl[\frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a\) , \( \frac{1}{5} a^{3} - \frac{6}{5} a^{2} - \frac{6}{5} a + 7\) , \( 1\) , \( \frac{3}{5} a^{3} - \frac{18}{5} a^{2} - \frac{13}{5} a + 16\) , \( \frac{9}{5} a^{3} - \frac{34}{5} a^{2} - \frac{24}{5} a + 20\bigr] \)
11.2-a2	\( \bigl[a\) , \( -a^{2} + a + 7\) , \( a\) , \( -\frac{26}{5} a^{3} - \frac{64}{5} a^{2} + \frac{106}{5} a + 48\) , \( 24 a^{3} + 50 a^{2} - 102 a - 187\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph