Elliptic curve isogeny class 49.1-a over number field 4.4.6125.1

• Base field: 4.4.6125.1
• Label: 4.4.6125.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

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-a over 4.4.6125.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[0\) , \( a^{3} + 2 a^{2} - 6 a - 7\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -2016 a^{3} - 2757 a^{2} + 11621 a + 9369\) , \( 55081 a^{3} + 75161 a^{2} - 318010 a - 256236\bigr] \)
49.1-a2	\( \bigl[0\) , \( -2 a^{3} - 3 a^{2} + 12 a + 13\) , \( a\) , \( 2 a^{3} - 7 a^{2} - 17 a + 54\) , \( -10 a^{3} + 15 a^{2} + 76 a - 133\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph