Elliptic curve isogeny class 225.1-m over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-225.1-m
• Conductor: 225.1
• Rank: \( 1 \)

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 225.1-m over 5.5.65657.1

Isogeny class 225.1-m contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
225.1-m1	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 8 a - 5\) , \( a^{3} - 4 a\) , \( -10 a^{4} + 14 a^{3} + 44 a^{2} - 34 a - 38\) , \( 16 a^{4} - 20 a^{3} - 75 a^{2} + 49 a + 68\bigr] \)
225.1-m2	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 8 a - 5\) , \( a^{3} - 4 a\) , \( 15 a^{4} - 6 a^{3} - 96 a^{2} + 31 a + 77\) , \( 101 a^{4} - 160 a^{3} - 393 a^{2} + 335 a + 383\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph