Elliptic curve isogeny class 49.10-b over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-49.10-b
• Conductor: 49.10
• 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 49.10-b over 4.4.8768.1

Isogeny class 49.10-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
49.10-b1	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 5 a - 4\) , \( a\) , \( 13 a^{3} - 74 a^{2} + 102 a + 7\) , \( -358 a^{3} + 1250 a^{2} - 90 a - 1869\bigr] \)
49.10-b2	\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 6 a^{3} - 27 a^{2} + 19 a + 26\) , \( -54 a^{3} + 186 a^{2} + 3 a - 309\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph