Elliptic curve isogeny class 12.1-b over number field 4.4.13824.1

• Base field: 4.4.13824.1
• Label: 4.4.13824.1-12.1-b
• Conductor: 12.1
• Rank: \( 0 \)

Base field 4.4.13824.1

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

Elliptic curves in class 12.1-b over 4.4.13824.1

Isogeny class 12.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 57 a^{3} + 20 a^{2} - 228 a - 194\) , \( -161 a^{3} - 434 a^{2} + 1023 a + 1475\bigr] \)
12.1-b2	\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{2} - 2\) , \( -15 a^{3} + 2 a^{2} + 58 a - 31\) , \( -17 a^{3} - 5 a^{2} + 59 a - 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph