Properties

Base field \(\Q(\sqrt{11}) \)
Label 2.2.44.1-275.1-g
Conductor 275.1
Rank not recorded

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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 not yet determined.

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