Elliptic curve isogeny class 11.2-c over number field 4.4.19025.1

• Base field: 4.4.19025.1
• Label: 4.4.19025.1-11.2-c
• 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-c over 4.4.19025.1

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

Curve label	Weierstrass Coefficients
11.2-c1	\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{63}{2} a^{3} + \frac{51}{2} a^{2} - 338 a - 498\) , \( 227 a^{3} + 171 a^{2} - 2478 a - 3633\bigr] \)
11.2-c2	\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 0\) , \( 3 a^{3} - \frac{25}{2} a^{2} - \frac{17}{2} a + 53\) , \( -22 a^{3} + \frac{203}{2} a^{2} + \frac{45}{2} a - 372\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph