Elliptic curve isogeny class 12.1-a over number field 4.4.8112.1

• Base field: 4.4.8112.1
• Label: 4.4.8112.1-12.1-a
• Conductor: 12.1
• Rank: \( 0 \)

Base field 4.4.8112.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 3 \); class number \(1\).

Elliptic curves in class 12.1-a over 4.4.8112.1

Isogeny class 12.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
12.1-a1	\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{2} - a + 4\) , \( a^{2} - 2\) , \( -178 a^{3} + 138 a^{2} + 778 a - 621\) , \( 10380 a^{3} - 24728 a^{2} + 2046 a + 9509\bigr] \)
12.1-a2	\( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a\) , \( -738 a^{3} + 1530 a^{2} + 516 a - 1068\bigr] \)
12.1-a3	\( \bigl[a + 1\) , \( a^{3} - 5 a\) , \( a^{2} - 3\) , \( -a^{3} - 2 a^{2} + 3 a + 4\) , \( -a^{3} - 2 a^{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph