Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 1.1-a contains 8 curves linked by isogenies of degrees dividing 28.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 40\) , \( 67 a + 177\bigr] \)
1.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 40\) , \( -67 a + 177\bigr] \)
1.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -270 a - 715\) , \( 3223 a + 8527\bigr] \)
1.1-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -270 a - 718\) , \( -3223 a - 8529\bigr] \)
1.1-a5	\( \bigl[a\) , \( -1\) , \( a\) , \( -255 a - 678\) , \( -3669 a - 9709\bigr] \)
1.1-a6	\( \bigl[a\) , \( -1\) , \( a\) , \( 255 a - 678\) , \( 3669 a - 9709\bigr] \)
1.1-a7	\( \bigl[1\) , \( -1\) , \( 1\) , \( 270 a - 715\) , \( -3223 a + 8527\bigr] \)
1.1-a8	\( \bigl[a\) , \( -1\) , \( a\) , \( 270 a - 718\) , \( 3223 a - 8529\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 7 & 4 & 28 & 14 & 2 & 28 & 4 \\ 7 & 1 & 28 & 4 & 2 & 14 & 4 & 28 \\ 4 & 28 & 1 & 28 & 14 & 2 & 7 & 4 \\ 28 & 4 & 28 & 1 & 2 & 14 & 4 & 7 \\ 14 & 2 & 14 & 2 & 1 & 7 & 2 & 14 \\ 2 & 14 & 2 & 14 & 7 & 1 & 14 & 2 \\ 28 & 4 & 7 & 4 & 2 & 14 & 1 & 28 \\ 4 & 28 & 4 & 7 & 14 & 2 & 28 & 1 \end{array}\right)\)

Isogeny graph