Elliptic curve isogeny class 1936.2-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1936.2-c
• Conductor: 1936.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 1936.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 1936.2-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
1936.2-c1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -31281\) , \( -2139919\bigr] \)
1936.2-c2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -199\bigr] \)
1936.2-c3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph