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

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

Isogeny class 2450.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2450.1-b1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -13 a - 22\) , \( 37 a + 51\bigr] \)
2450.1-b2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -213 a - 342\) , \( 2277 a + 3075\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph