Elliptic curve isogeny class 16.1-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 16.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 0\) , \( -1\bigr] \)
16.1-a2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a + 4\) , \( 8\bigr] \)
16.1-a3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a - 36\) , \( -66 a + 182\bigr] \)
16.1-a4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -15 a - 40\) , \( 26 a + 68\bigr] \)

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