Elliptic curve isogeny class 7.2-a over number field 4.4.13888.1

• Base field: 4.4.13888.1
• Label: 4.4.13888.1-7.2-a
• Conductor: 7.2
• Rank: \( 0 \)

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 7.2-a over 4.4.13888.1

Isogeny class 7.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.2-a1	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( 0\) , \( a^{2} - a - 4\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{4}{3} a - 6\) , \( a^{3} - 4 a - 1\bigr] \)
7.2-a2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -a^{2} + a + 5\) , \( 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{16}{3} a + 8\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - \frac{11}{3} a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph