Elliptic curve isogeny class 3375.10-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-3375.10-b
• Conductor: 3375.10
• Rank: \( 1 \)

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

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

Elliptic curves in class 3375.10-b over \(\Q(\sqrt{-11}) \)

Isogeny class 3375.10-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
3375.10-b1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -39 a + 1\) , \( 101 a - 91\bigr] \)
3375.10-b2	\( \bigl[1\) , \( -a\) , \( a\) , \( 2 a + 65\) , \( -151 a + 95\bigr] \)
3375.10-b3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -4 a - 64\) , \( 183 a - 629\bigr] \)
3375.10-b4	\( \bigl[1\) , \( -a\) , \( a\) , \( 37 a\) , \( -344 a - 93\bigr] \)
3375.10-b5	\( \bigl[1\) , \( -a\) , \( a\) , \( -278 a - 540\) , \( -3566 a - 4170\bigr] \)
3375.10-b6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 346 a + 411\) , \( 2093 a - 9319\bigr] \)
3375.10-b7	\( \bigl[1\) , \( -a\) , \( a\) , \( 912 a - 500\) , \( -10094 a - 9468\bigr] \)
3375.10-b8	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 206 a - 1579\) , \( 3981 a - 24011\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 6 & 12 & 4 & 12 & 4 \\ 3 & 1 & 6 & 2 & 4 & 12 & 4 & 12 \\ 2 & 6 & 1 & 3 & 6 & 2 & 6 & 2 \\ 6 & 2 & 3 & 1 & 2 & 6 & 2 & 6 \\ 12 & 4 & 6 & 2 & 1 & 12 & 4 & 3 \\ 4 & 12 & 2 & 6 & 12 & 1 & 3 & 4 \\ 12 & 4 & 6 & 2 & 4 & 3 & 1 & 12 \\ 4 & 12 & 2 & 6 & 3 & 4 & 12 & 1 \end{array}\right)\)

Isogeny graph