Elliptic curve isogeny class 2450.3-g over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2450.3-g
• Conductor: 2450.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2450.3-g over \(\Q(\sqrt{2}) \)

Isogeny class 2450.3-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2450.3-g1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -28 a - 3180\) , \( 49882 a - 67\bigr] \)
2450.3-g2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -3 a\) , \( -6 a - 7\bigr] \)
2450.3-g3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 22 a - 5\) , \( 177 a + 123\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph