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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-1764.2-c
• 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-c over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
1764.2-c1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -60 a + 71\) , \( -56 a + 457\bigr] \)
1764.2-c2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -410 a - 339\) , \( 5854 a - 493\bigr] \)
1764.2-c3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -60 a + 51\) , \( 24 a + 509\bigr] \)
1764.2-c4	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 290 a + 121\) , \( -606 a + 4919\bigr] \)

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