Elliptic curve isogeny class 81.1-c over number field 4.4.14272.1

• Base field: 4.4.14272.1
• Label: 4.4.14272.1-81.1-c
• Conductor: 81.1
• Rank: \( 0 \)

Base field 4.4.14272.1

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

Elliptic curves in class 81.1-c over 4.4.14272.1

Isogeny class 81.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
81.1-c1	\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( 0\) , \( a^{3} - 3 a^{2} - a + 3\) , \( 21 a^{3} - 79 a^{2} - 3 a + 43\) , \( 129 a^{3} - 480 a^{2} + 291\bigr] \)
81.1-c2	\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -2 a^{3} + 5 a^{2} + 6 a - 3\) , \( 1\) , \( 83 a^{3} - 82 a^{2} - 520 a - 304\) , \( -787 a^{3} + 877 a^{2} + 4684 a + 2609\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph