Elliptic curve isogeny class 92.2-c over number field 4.4.10304.1

• Base field: 4.4.10304.1
• Label: 4.4.10304.1-92.2-c
• Number of curves: 2
• Conductor: 92.2
• Rank: \( 0 \)

Base field 4.4.10304.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 8 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 92.2-c over 4.4.10304.1

Isogeny class 92.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
92.2-c1	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{17}{2} a^{3} - 21 a^{2} + \frac{517}{2} a - 337\) , \( \frac{1331}{2} a^{3} - \frac{4575}{2} a^{2} - 1010 a + 5035\bigr] \)
92.2-c2	\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{5}{2} a^{3} + a^{2} + \frac{39}{2} a + 13\) , \( -\frac{15}{2} a^{3} + a^{2} + \frac{105}{2} a + 33\bigr] \)