Elliptic curve isogeny class 49.1-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 49.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 49.1-a contains 8 curves linked by isogenies of degrees dividing 28.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( 1\bigr] \)
49.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
49.1-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 105 a - 317\) , \( -1015 a + 2752\bigr] \)
49.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 105 a - 317\) , \( 1015 a - 2752\bigr] \)
49.1-a5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -37\) , \( 78\bigr] \)
49.1-a6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
49.1-a7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -105 a - 317\) , \( 1015 a + 2752\bigr] \)
49.1-a8	\( \bigl[1\) , \( -1\) , \( 0\) , \( -105 a - 317\) , \( -1015 a - 2752\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph