Elliptic curve isogeny class 49.1-b over number field 4.4.6125.1

• Base field: 4.4.6125.1
• Label: 4.4.6125.1-49.1-b
• Conductor: 49.1
• Rank: \( 2 \)

Base field 4.4.6125.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 9 x^{2} + 9 x + 11 \); class number \(1\).

Elliptic curves in class 49.1-b over 4.4.6125.1

Isogeny class 49.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[0\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 1\) , \( 30 a^{3} + 30 a^{2} - 180 a - 149\) , \( 102 a^{3} + 102 a^{2} - 612 a - 492\bigr] \)
49.1-b2	\( \bigl[0\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 1\) , \( 1\) , \( 0\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph