Elliptic curve isogeny class 37.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-37.1-a
• Conductor: 37.1
• Rank: \( 0 \)

Base field 5.5.65657.1

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

Elliptic curves in class 37.1-a over 5.5.65657.1

Isogeny class 37.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
37.1-a1	\( \bigl[0\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - a - 2\) , \( 345 a^{4} - 549 a^{3} - 1365 a^{2} + 1487 a + 783\) , \( 3135 a^{4} - 5551 a^{3} - 12034 a^{2} + 14521 a + 5015\bigr] \)
37.1-a2	\( \bigl[0\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 49 a^{4} - 88 a^{3} - 178 a^{2} + 239 a + 64\) , \( 162 a^{4} - 287 a^{3} - 588 a^{2} + 779 a + 208\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph