Elliptic curve isogeny class 3.1-b over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-3.1-b
• Conductor: 3.1
• Rank: \( 0 \)

Base field 4.4.9909.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 3 x + 3 \); class number \(1\).

Elliptic curves in class 3.1-b over 4.4.9909.1

Isogeny class 3.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3.1-b1	\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 0\) , \( 60 a^{3} + 24 a^{2} - 336 a - 336\) , \( -6 a^{3} - 33 a^{2} + 75 a + 129\bigr] \)
3.1-b2	\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 0\) , \( -15 a^{3} - 6 a^{2} + 84 a + 84\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph