Elliptic curve isogeny class 2450.2-f over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2450.2-f
• Conductor: 2450.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 2450.2-f over \(\Q(\sqrt{2}) \)

Isogeny class 2450.2-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
2450.2-f1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 916 a - 1537\) , \( -38048 a + 52250\bigr] \)
2450.2-f2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 14 a - 81\) , \( -380 a - 187\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph