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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-13122.5-d
• Conductor: 13122.5
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
13122.5-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1077\) , \( 13877\bigr] \)
13122.5-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -42\) , \( -100\bigr] \)
13122.5-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -852\) , \( 19664\bigr] \)
13122.5-d4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \)

Rank

Rank: \( 1 \)

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