Elliptic curve isogeny class 4.1-a over number field 4.4.19225.1

• Base field: 4.4.19225.1
• Label: 4.4.19225.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

Base field 4.4.19225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 15 x^{2} + 2 x + 44 \); class number \(1\).

Elliptic curves in class 4.1-a over 4.4.19225.1

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

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{3}{2} a + 15\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( 22 a^{3} + 21 a^{2} - 296 a - 524\) , \( -\frac{351}{2} a^{3} - \frac{307}{2} a^{2} + \frac{4657}{2} a + 4034\bigr] \)
4.1-a2	\( \bigl[a + 1\) , \( a^{3} - 4 a^{2} - 5 a + 22\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a^{2} + \frac{25}{2} a - 15\) , \( a^{3} - 3 a^{2} - 3 a + 22\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph