Elliptic curve isogeny class 16562.1-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-16562.1-c
• Conductor: 16562.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 16562.1-c over \(\Q(\sqrt{-2}) \)

Isogeny class 16562.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16562.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \)
16562.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \)
16562.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \)
16562.1-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \)

Rank

Rank: \( 0 \)

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