Elliptic curve isogeny class 324.1-f over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-324.1-f
• Conductor: 324.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.1-f over \(\Q(\sqrt{7}) \)

Isogeny class 324.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
324.1-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \)
324.1-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \)
324.1-f3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -178 a - 472\) , \( -2520 a - 6668\bigr] \)
324.1-f4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -1618 a - 4282\) , \( 53040 a + 140330\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph