Elliptic curve isogeny class 275.1-d over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-275.1-d
• Conductor: 275.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{11}) \)

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

Elliptic curves in class 275.1-d over \(\Q(\sqrt{11}) \)

Isogeny class 275.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
275.1-d1	\( \bigl[a\) , \( 1\) , \( a\) , \( 135 a - 500\) , \( 1826 a - 6344\bigr] \)
275.1-d2	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
275.1-d3	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -8\bigr] \)
275.1-d4	\( \bigl[a\) , \( 1\) , \( a\) , \( -30\) , \( 22\bigr] \)
275.1-d5	\( \bigl[a\) , \( 1\) , \( a\) , \( -60\) , \( -250\bigr] \)
275.1-d6	\( \bigl[a\) , \( 1\) , \( a\) , \( -135 a - 500\) , \( -1826 a - 6344\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph