Elliptic curve isogeny class 41.1-c over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-41.1-c
• Conductor: 41.1
• Rank: \( 0 \)

Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 41.1-c over 4.4.5125.1

Isogeny class 41.1-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
41.1-c1	\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 0\) , \( 0\bigr] \)
41.1-c2	\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( -10 a^{2} + 10 a\) , \( -31 a^{2} + 31 a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph