Elliptic curve isogeny class 12.2-a over number field 4.4.18097.1

• Base field: 4.4.18097.1
• Label: 4.4.18097.1-12.2-a
• Conductor: 12.2
• Rank: \( 0 \)

Base field 4.4.18097.1

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

Elliptic curves in class 12.2-a over 4.4.18097.1

Isogeny class 12.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.2-a1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -8 a^{3} - 10 a^{2} + 28 a + 8\) , \( -46 a^{3} - 75 a^{2} + 133 a + 82\bigr] \)
12.2-a2	\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + 2 a^{2} - 14 a - 8\) , \( -7 a^{3} + 36 a + 15\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph