Elliptic curve isogeny class 31.1-b over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-31.1-b
• Conductor: 31.1
• 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 31.1-b over 4.4.5725.1

Isogeny class 31.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
31.1-b1	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( 0\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{11}{3} a^{3} - \frac{28}{3} a - \frac{25}{3}\) , \( -\frac{31}{3} a^{3} + 54 a^{2} - \frac{70}{3} a - \frac{235}{3}\bigr] \)
31.1-b2	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( 0\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{11}{3} a^{3} - 5 a^{2} - \frac{13}{3} a + \frac{5}{3}\) , \( -\frac{17}{3} a^{3} + 28 a^{2} - \frac{32}{3} a - \frac{122}{3}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph