Elliptic curve isogeny class 28.3-a over number field 4.4.13888.1

• Base field: 4.4.13888.1
• Label: 4.4.13888.1-28.3-a
• Conductor: 28.3
• 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 28.3-a over 4.4.13888.1

Isogeny class 28.3-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
28.3-a1	\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{37}{3} a^{3} + \frac{200}{3} a^{2} + \frac{208}{3} a - 237\) , \( -\frac{293}{3} a^{3} + \frac{925}{3} a^{2} + \frac{1838}{3} a - 1362\bigr] \)
28.3-a2	\( \bigl[a\) , \( a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{35}{3} a^{3} - \frac{136}{3} a^{2} + \frac{25}{3} a + 54\) , \( -83 a^{3} + 329 a^{2} - 60 a - 385\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph