Elliptic curve isogeny class 12.1-a over number field 4.4.18736.1

• Base field: 4.4.18736.1
• Label: 4.4.18736.1-12.1-a
• Conductor: 12.1
• Rank: \( 1 \)

Base field 4.4.18736.1

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

Elliptic curves in class 12.1-a over 4.4.18736.1

Isogeny class 12.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
12.1-a1	\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( a + 1\) , \( -3 a^{3} + 18 a^{2} + 12 a - 36\) , \( -11 a^{3} + 52 a^{2} + 34 a - 113\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph