Elliptic curve isogeny class 49.4-c over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-49.4-c
• Conductor: 49.4
• Rank: \( 0 \)

Base field 4.4.4205.1

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

Elliptic curves in class 49.4-c over 4.4.4205.1

Isogeny class 49.4-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
49.4-c1	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 8 a + 1\) , \( a + 1\) , \( 66 a^{3} - 37 a^{2} - 364 a - 233\) , \( -457 a^{3} + 318 a^{2} + 2384 a + 1238\bigr] \)
49.4-c2	\( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 8 a\) , \( a^{3} - a^{2} - 4 a\) , \( 34 a^{3} - 57 a^{2} - 134 a + 56\) , \( -82 a^{3} + 135 a^{2} + 322 a - 128\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph