Elliptic curve isogeny class 10.1-d over number field 4.4.6224.1

• Base field: 4.4.6224.1
• Label: 4.4.6224.1-10.1-d
• Conductor: 10.1
• Rank: \( 0 \)

Base field 4.4.6224.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 2 x + 5 \); class number \(1\).

Elliptic curves in class 10.1-d over 4.4.6224.1

Isogeny class 10.1-d contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
10.1-d1	\( \bigl[a\) , \( -a^{3} + 5 a\) , \( a^{2} - 3\) , \( 3 a^{3} - 7 a^{2} - 9 a + 13\) , \( 2 a^{3} - 2\bigr] \)
10.1-d2	\( \bigl[a\) , \( -a^{3} + 5 a\) , \( a^{2} - 3\) , \( 5293 a^{3} - 10877 a^{2} - 11229 a + 13113\) , \( 465056 a^{3} - 894282 a^{2} - 1103684 a + 1211518\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph