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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2450.1-f
• Conductor: 2450.1
• Rank: \( 0 \)

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

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

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

Isogeny class 2450.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2450.1-f1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -3 a + 2\) , \( 18 a - 25\bigr] \)
2450.1-f2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 158 a + 199\) , \( -11 a - 59\bigr] \)
2450.1-f3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -467 a - 1051\) , \( -1511 a - 5059\bigr] \)
2450.1-f4	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 47 a - 98\) , \( 258 a - 305\bigr] \)

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