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

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-275.1-g
• Conductor: 275.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
275.1-g1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 135 a - 499\) , \( -1691 a + 5844\bigr] \)
275.1-g2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
275.1-g3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \)
275.1-g4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \)
275.1-g5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \)
275.1-g6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -135 a - 499\) , \( 1691 a + 5844\bigr] \)

Rank

Rank: \( 0 \)

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