Elliptic curve isogeny class 11.2-c over number field 4.4.11525.1

• Base field: 4.4.11525.1
• Label: 4.4.11525.1-11.2-c
• Conductor: 11.2
• Rank: \( 1 \)

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-c over 4.4.11525.1

Isogeny class 11.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
11.2-c1	\( \bigl[\frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a + 1\) , \( a^{2} - 2 a - 6\) , \( \frac{1}{5} a^{3} + \frac{4}{5} a^{2} - \frac{11}{5} a - 6\) , \( -\frac{1357}{5} a^{3} + \frac{3592}{5} a^{2} + \frac{8862}{5} a - 4160\) , \( -\frac{31887}{5} a^{3} + \frac{83412}{5} a^{2} + \frac{214607}{5} a - 99797\bigr] \)
11.2-c2	\( \bigl[a + 1\) , \( -a^{2} + 2 a + 7\) , \( \frac{1}{5} a^{3} + \frac{4}{5} a^{2} - \frac{11}{5} a - 5\) , \( -\frac{88}{5} a^{3} - \frac{87}{5} a^{2} + \frac{813}{5} a + 242\) , \( -\frac{267}{5} a^{3} - \frac{168}{5} a^{2} + \frac{2407}{5} a + 550\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph