Elliptic curve isogeny class 31.1-b over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-31.1-b
• Conductor: 31.1
• Rank: \( 0 \)

Base field 4.4.5744.1

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

Elliptic curves in class 31.1-b over 4.4.5744.1

Isogeny class 31.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
31.1-b1	\( \bigl[a\) , \( 2 a^{3} - a^{2} - 10 a + 1\) , \( a^{2} - 2\) , \( 3 a^{3} - 3 a^{2} - 16 a + 6\) , \( 2 a^{3} - 2 a^{2} - 10 a + 2\bigr] \)
31.1-b2	\( \bigl[1\) , \( 2 a^{3} - a^{2} - 8 a\) , \( a^{3} - 5 a\) , \( -15 a^{3} + 23 a^{2} + 61 a - 74\) , \( -144 a^{3} + 120 a^{2} + 633 a - 248\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph