Elliptic curve isogeny class 12.1-b over number field 4.4.15952.1

• Base field: 4.4.15952.1
• Label: 4.4.15952.1-12.1-b
• Conductor: 12.1
• Rank bounds: 0...1

Base field 4.4.15952.1

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

Elliptic curves in class 12.1-b over 4.4.15952.1

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

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( -8 a^{3} + 60 a - 15\) , \( -41 a^{3} + 11 a^{2} + 271 a - 77\bigr] \)
12.1-b2	\( \bigl[a^{3} - 5 a\) , \( -2 a^{3} + a^{2} + 10 a - 2\) , \( -a^{3} + a^{2} + 6 a - 2\) , \( -68 a^{3} + 43 a^{2} + 379 a - 106\) , \( 28 a^{3} - 18 a^{2} - 157 a + 44\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph