Elliptic curve isogeny class 7.4-b over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-7.4-b
• Conductor: 7.4
• Rank: \( 1 \)

Base field 4.4.8768.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7 \); class number \(1\).

Elliptic curves in class 7.4-b over 4.4.8768.1

Isogeny class 7.4-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.4-b1	\( \bigl[a^{3} - 4 a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - 3\) , \( -8 a^{3} + 13 a^{2} + 31 a - 20\) , \( -11 a^{3} + 22 a^{2} + 39 a - 46\bigr] \)
7.4-b2	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 3 a^{2} - 2 a + 10\) , \( -3 a^{3} + 11 a^{2} + 5 a - 36\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph