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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2450.1-i
• 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-i over \(\Q(\sqrt{2}) \)

Isogeny class 2450.1-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2450.1-i1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 1425 a - 2268\) , \( 37120 a - 54319\bigr] \)
2450.1-i2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \)
2450.1-i3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \)
2450.1-i4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \)
2450.1-i5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \)
2450.1-i6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1425 a - 2268\) , \( -37120 a - 54319\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph