Elliptic curve isogeny class 441.2-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-441.2-d
• Conductor: 441.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.2-d over \(\Q(\sqrt{2}) \)

Isogeny class 441.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
441.2-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a - 4\) , \( -10 a - 3\bigr] \)
441.2-d2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -101 a - 74\) , \( 277 a + 221\bigr] \)
441.2-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -26 a - 59\) , \( -134 a - 214\bigr] \)
441.2-d4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -431 a - 924\) , \( -7681 a - 13013\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph