Elliptic curve isogeny class 72.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-72.1-a
• Conductor: 72.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 72.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 72.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -231 a + 793\) , \( 26226 a - 86955\bigr] \)
72.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -62 a - 208\) , \( 197 a + 652\bigr] \)
72.1-a4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 369 a - 1197\) , \( 6480 a - 21465\bigr] \)
72.1-a5	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 969 a - 3187\) , \( -30024 a + 99605\bigr] \)
72.1-a6	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5769 a - 19107\) , \( 432054 a - 1432935\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph