Elliptic curve isogeny class 12.1-a over number field 4.4.14272.1

• Base field: 4.4.14272.1
• Label: 4.4.14272.1-12.1-a
• Conductor: 12.1
• Rank: \( 0 \)

Base field 4.4.14272.1

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

Elliptic curves in class 12.1-a over 4.4.14272.1

Isogeny class 12.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
12.1-a1	\( \bigl[a\) , \( 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 36 a^{3} - 41 a^{2} - 213 a - 116\) , \( -230 a^{3} + 257 a^{2} + 1373 a + 758\bigr] \)
12.1-a2	\( \bigl[a\) , \( 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 6 a^{3} - 6 a^{2} - 33 a - 41\) , \( -608 a^{3} + 679 a^{2} + 3638 a + 1967\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph