Elliptic curve isogeny class 4624.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4624.1-c
• Conductor: 4624.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}) \)

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

Elliptic curves in class 4624.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 4624.1-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
4624.1-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 920 a - 1452\) , \( 19120 a - 28104\bigr] \)
4624.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 1420 a - 772\) , \( 25080 a - 18520\bigr] \)
4624.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -12\) , \( -8\bigr] \)
4624.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -452\) , \( 2632\bigr] \)
4624.1-c5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1420 a - 772\) , \( -25080 a - 18520\bigr] \)
4624.1-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -172\) , \( -840\bigr] \)
4624.1-c7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -412\) , \( 3288\bigr] \)
4624.1-c8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -920 a - 1452\) , \( -19120 a - 28104\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\ 3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\ 4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\ 6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\ 12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\ 2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\ 12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\ 4 & 12 & 4 & 6 & 3 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph