Elliptic curve isogeny class 36.3-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-36.3-a
• Conductor: 36.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.3-a over \(\Q(\sqrt{7}) \)

Isogeny class 36.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.3-a1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a + 4\) , \( 0\bigr] \)
36.3-a2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 65 a + 172\) , \( 0\bigr] \)
36.3-a3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -260 a - 688\) , \( -604 a - 1598\bigr] \)
36.3-a4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4 a - 16\) , \( -4 a - 2\bigr] \)

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