Elliptic curve isogeny class 6.1-c over number field 4.4.13824.1

• Base field: 4.4.13824.1
• Label: 4.4.13824.1-6.1-c
• Conductor: 6.1
• Rank: \( 0 \)

Base field 4.4.13824.1

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

Elliptic curves in class 6.1-c over 4.4.13824.1

Isogeny class 6.1-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
6.1-c1	\( \bigl[1\) , \( -a^{3} + 5 a + 1\) , \( a\) , \( 17 a^{3} + 10 a^{2} - 72 a - 66\) , \( 86 a^{3} + 115 a^{2} - 426 a - 504\bigr] \)
6.1-c2	\( \bigl[1\) , \( a^{3} - 5 a + 1\) , \( 0\) , \( 765 a^{3} + 2310 a^{2} - 290 a - 3690\) , \( 27896 a^{3} + 52051 a^{2} - 44429 a - 55800\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph