Elliptic curve isogeny class 27.2-d over number field 4.4.14272.1

• Base field: 4.4.14272.1
• Label: 4.4.14272.1-27.2-d
• Conductor: 27.2
• Rank: \( 1 \)

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 27.2-d over 4.4.14272.1

Isogeny class 27.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.2-d1	\( \bigl[1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 6 a^{3} - 22 a^{2} + 2 a + 22\) , \( 30 a^{3} - 105 a^{2} + 6 a + 58\bigr] \)
27.2-d2	\( \bigl[1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 581 a^{3} - 1997 a^{2} - 38 a + 1222\) , \( 15566 a^{3} - 53503 a^{2} - 937 a + 32479\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph