Elliptic curve isogeny class 3.1-a over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-3.1-a
• 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-a over 4.4.9909.1

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

Curve label	Weierstrass Coefficients
3.1-a1	\( \bigl[a^{3} - 4 a - 2\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} - 28 a^{2} - 26 a + 32\) , \( -85 a^{3} + 160 a^{2} + 209 a - 133\bigr] \)
3.1-a2	\( \bigl[a + 1\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( 358 a^{3} + 180 a^{2} - 2067 a - 2129\) , \( 836 a^{3} + 427 a^{2} - 4792 a - 4938\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph