Elliptic curve isogeny class 8.3-b over number field 4.4.15188.1

• Base field: 4.4.15188.1
• Label: 4.4.15188.1-8.3-b
• Conductor: 8.3
• Rank: \( 1 \)

Base field 4.4.15188.1

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

Elliptic curves in class 8.3-b over 4.4.15188.1

Isogeny class 8.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.3-b1	\( \bigl[a^{3} - a^{2} - 5 a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{229}{2} a^{3} - 388 a^{2} + \frac{29}{2} a + 112\) , \( 2783 a^{3} - 8994 a^{2} + 127 a + 2558\bigr] \)
8.3-b2	\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( a^{3} - a^{2} - 7 a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( -\frac{1}{2} a^{3} - 2 a^{2} + \frac{1}{2} a + 6\) , \( -5 a^{2} - 11 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph