Elliptic curve isogeny class 7.1-b over number field 4.4.13888.1

• Base field: 4.4.13888.1
• Label: 4.4.13888.1-7.1-b
• Conductor: 7.1
• Rank: \( 1 \)

Base field 4.4.13888.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 6 x + 9 \); class number \(1\).

Elliptic curves in class 7.1-b over 4.4.13888.1

Isogeny class 7.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
7.1-b1	\( \bigl[a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( \frac{5}{3} a^{3} - \frac{7}{3} a^{2} - \frac{5}{3} a + 2\) , \( -\frac{16}{3} a^{3} + \frac{29}{3} a^{2} + \frac{100}{3} a + 18\bigr] \)
7.1-b2	\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( a^{2} - 2 a - 5\) , \( a\) , \( -\frac{4}{3} a^{3} - \frac{1}{3} a^{2} + \frac{13}{3} a + 2\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} + \frac{10}{3} a + 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph