Elliptic curve isogeny class 41.1-d over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-41.1-d
• 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-d over 4.4.5125.1

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

Curve label	Weierstrass Coefficients
41.1-d1	\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 144 a^{3} - 153 a^{2} - 559 a - 225\) , \( -1890 a^{3} + 1126 a^{2} + 8698 a + 5670\bigr] \)
41.1-d2	\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 4 a^{3} - 3 a^{2} - 19 a - 5\) , \( 11 a^{3} + a^{2} - 64 a - 61\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph