Elliptic curve isogeny class 45.1-c over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-45.1-c
• Conductor: 45.1
• 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 45.1-c over 5.5.65657.1

Isogeny class 45.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
45.1-c1	\( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{3} - 3 a\) , \( 2 a^{4} - 4 a^{3} - 11 a^{2} + 13 a + 13\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 5 a + 6\bigr] \)
45.1-c2	\( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 5\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 9\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\) , \( 24 a^{4} - 31 a^{3} - 110 a^{2} + 79 a + 89\) , \( 93 a^{4} - 125 a^{3} - 415 a^{2} + 318 a + 327\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph