Elliptic curve isogeny class 83.1-c over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-83.1-c
• Conductor: 83.1
• Rank: \( 1 \)

Base field 5.5.24217.1

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

Elliptic curves in class 83.1-c over 5.5.24217.1

Isogeny class 83.1-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
83.1-c1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a^{2} + a - 1\) , \( -39 a^{4} + 29 a^{3} + 175 a^{2} - 93 a - 113\) , \( -50 a^{4} + 54 a^{3} + 221 a^{2} - 215 a - 280\bigr] \)
83.1-c2	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( a^{2} + a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -a^{3} - a^{2} + 3 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph