Elliptic curve isogeny class 11.2-d over number field 4.4.11525.1

• Base field: 4.4.11525.1
• Label: 4.4.11525.1-11.2-d
• 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-d over 4.4.11525.1

Isogeny class 11.2-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
11.2-d1	\( \bigl[\frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{6}{5} a\) , \( -\frac{1}{5} a^{3} + \frac{1}{5} a^{2} + \frac{11}{5} a\) , \( \frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a + 1\) , \( -\frac{21}{5} a^{3} - \frac{69}{5} a^{2} + \frac{101}{5} a + 51\) , \( \frac{121}{5} a^{3} + \frac{204}{5} a^{2} - \frac{461}{5} a - 152\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph