Elliptic curve isogeny class 2450.1-m over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2450.1-m
• Conductor: 2450.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2450.1-m over \(\Q(\sqrt{2}) \)

Isogeny class 2450.1-m contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
2450.1-m1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -589 a - 3844\) , \( -20724 a - 93386\bigr] \)
2450.1-m2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 56 a - 114\) , \( -309 a + 560\bigr] \)
2450.1-m3	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 161 a + 31\) , \( -649 a + 39\bigr] \)
2450.1-m4	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -29 a - 29\) , \( -39 a + 15\bigr] \)
2450.1-m5	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -9 a - 24\) , \( 36 a + 64\bigr] \)
2450.1-m6	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -1629 a - 2404\) , \( -42084 a - 61450\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph