Elliptic curve isogeny class 2304.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2304.1-c
• Conductor: 2304.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2304.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 2304.1-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2304.1-c1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -408 a - 1632\) , \( 18804 a + 13548\bigr] \)
2304.1-c2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 48\) , \( 900 a + 1260\bigr] \)
2304.1-c3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 3\) , \( 0\bigr] \)
2304.1-c4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a - 12\) , \( -20 a + 28\bigr] \)
2304.1-c5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a - 72\) , \( 180 a + 252\bigr] \)
2304.1-c6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -128 a - 192\) , \( -1100 a - 1540\bigr] \)
2304.1-c7	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a - 1152\) , \( 13860 a - 19404\bigr] \)
2304.1-c8	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 408 a - 1632\) , \( 18804 a - 13548\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph