Elliptic curve isogeny class 11.2-a over number field 4.4.19025.1

• Base field: 4.4.19025.1
• Label: 4.4.19025.1-11.2-a
• Conductor: 11.2
• Rank: \( 0 \)

Base field 4.4.19025.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 44 \); class number \(1\).

Elliptic curves in class 11.2-a over 4.4.19025.1

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

Curve label	Weierstrass Coefficients
11.2-a1	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -361 a^{3} + 394 a^{2} + 2499 a - 2374\) , \( -9488 a^{3} + \frac{19673}{2} a^{2} + \frac{131449}{2} a - 58840\bigr] \)
11.2-a2	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( \frac{3}{2} a^{3} + a^{2} - \frac{21}{2} a - 8\) , \( 5 a^{3} - \frac{17}{2} a^{2} - \frac{43}{2} a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph