Elliptic curve isogeny class 1764.2-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-1764.2-b
• Conductor: 1764.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1764.2-b over \(\Q(\sqrt{-11}) \)

Isogeny class 1764.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1764.2-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 58 a + 12\) , \( 55 a + 402\bigr] \)
1764.2-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 408 a - 748\) , \( -5855 a + 5362\bigr] \)
1764.2-b3	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 58 a - 8\) , \( -25 a + 534\bigr] \)
1764.2-b4	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -292 a + 412\) , \( 605 a + 4314\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph