Elliptic curve isogeny class 13122.5-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-13122.5-e
• Conductor: 13122.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 13122.5-e over \(\Q(\sqrt{-2}) \)

Isogeny class 13122.5-e contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
13122.5-e1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -9695\) , \( -364985\bigr] \)
13122.5-e2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \)
13122.5-e3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \)
13122.5-e4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 25\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph