Elliptic curve isogeny class 63.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-63.1-b
• Conductor: 63.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 63.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 63.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
63.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -35\) , \( 182\bigr] \)
63.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( 115 a - 320\) , \( 1198 a - 3392\bigr] \)
63.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
63.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -4\bigr] \)
63.1-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( -40\) , \( -130\bigr] \)
63.1-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -50\) , \( 86\bigr] \)
63.1-b7	\( \bigl[a\) , \( 1\) , \( a\) , \( -115 a - 320\) , \( -1198 a - 3392\bigr] \)
63.1-b8	\( \bigl[a\) , \( 1\) , \( a\) , \( -785\) , \( 7730\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph