Elliptic curve isogeny class 361.1-d over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-361.1-d
• Conductor: 361.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 361.1-d over \(\Q(\sqrt{11}) \)

Isogeny class 361.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
361.1-d1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -7 a - 27\) , \( 15 a + 47\bigr] \)
361.1-d2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 58 a + 188\) , \( -163 a - 544\bigr] \)
361.1-d3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -59 a + 188\) , \( 163 a - 544\bigr] \)
361.1-d4	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 6 a - 27\) , \( -15 a + 47\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph