Elliptic curve isogeny class 4.1-b over number field 4.4.18097.1

• Base field: 4.4.18097.1
• Label: 4.4.18097.1-4.1-b
• Conductor: 4.1
• Rank: \( 0 \)

Base field 4.4.18097.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 6 x + 4 \); class number \(1\).

Elliptic curves in class 4.1-b over 4.4.18097.1

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1131}{2} a^{3} + \frac{1881}{2} a^{2} + \frac{7159}{2} a - 5779\) , \( -\frac{39037}{2} a^{3} + \frac{58751}{2} a^{2} + \frac{247527}{2} a - 179770\bigr] \)
4.1-b2	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 4 a\) , \( -2 a^{2} + 5\) , \( \frac{11}{2} a^{3} - \frac{5}{2} a^{2} - \frac{61}{2} a - 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph