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

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

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

Curve label	Weierstrass Coefficients
2450.1-c1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -192 a - 299\) , \( -1843 a - 2677\bigr] \)
2450.1-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 9 a - 12\) , \( -5 a + 7\bigr] \)
2450.1-c3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -42 a - 69\) , \( -123 a - 167\bigr] \)
2450.1-c4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 264 a - 642\) , \( 2875 a - 5873\bigr] \)

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