Elliptic curve isogeny class 37.1-a over number field 5.5.36497.1

• Base field: 5.5.36497.1
• Label: 5.5.36497.1-37.1-a
• Conductor: 37.1
• Rank: \( 0 \)

Base field 5.5.36497.1

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

Elliptic curves in class 37.1-a over 5.5.36497.1

Isogeny class 37.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
37.1-a1	\( \bigl[a\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 32 a^{4} - 13 a^{3} - 148 a^{2} - 4 a + 30\) , \( 154 a^{4} - 69 a^{3} - 676 a^{2} - 48 a + 128\bigr] \)
37.1-a2	\( \bigl[a\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 6 a + 5\) , \( -a^{3} + 2 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph