Elliptic curve isogeny class 13475.3-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-13475.3-b
• Conductor: 13475.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 13475.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 13475.3-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
13475.3-b1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 269 a - 90\) , \( -1449 a - 1977\bigr] \)
13475.3-b2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 149 a - 50\) , \( -2549 a - 4152\bigr] \)
13475.3-b3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -1321 a + 440\) , \( 64581 a + 110263\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph