Elliptic curve isogeny class 19600.1-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-19600.1-d
• Conductor: 19600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 19600.1-d over \(\Q(\sqrt{-2}) \)

Isogeny class 19600.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
19600.1-d1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 10\) , \( -22\bigr] \)
19600.1-d2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -70\) , \( -150\bigr] \)
19600.1-d3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -350\) , \( 2538\bigr] \)
19600.1-d4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1070\) , \( -12950\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph