Elliptic curve isogeny class 31.2-b over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-31.2-b
• Conductor: 31.2
• Rank: \( 1 \)

Base field 4.4.5725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 11 \); class number \(1\).

Elliptic curves in class 31.2-b over 4.4.5725.1

Isogeny class 31.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
31.2-b1	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( \frac{41}{3} a^{3} + 17 a^{2} - \frac{223}{3} a - \frac{241}{3}\) , \( -\frac{16}{3} a^{3} + 5 a^{2} + \frac{191}{3} a + \frac{137}{3}\bigr] \)
31.2-b2	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( \frac{31}{3} a^{3} + 12 a^{2} - \frac{158}{3} a - \frac{146}{3}\) , \( -39 a^{3} - 21 a^{2} + 278 a + 223\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph