Elliptic curve isogeny class 6.1-d over number field 4.4.13768.1

• Base field: 4.4.13768.1
• Label: 4.4.13768.1-6.1-d
• Conductor: 6.1
• Rank: \( 1 \)

Base field 4.4.13768.1

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

Elliptic curves in class 6.1-d over 4.4.13768.1

Isogeny class 6.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
6.1-d1	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( a\) , \( -5 a^{3} + 10 a^{2} + 21 a - 30\) , \( -16 a^{3} + 22 a^{2} + 70 a - 56\bigr] \)
6.1-d2	\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 4 a - 1\) , \( -a^{2} + 4\) , \( -2 a^{3} + 7 a^{2} - 5 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph