Elliptic curve isogeny class 10000.1-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-10000.1-f
• Conductor: 10000.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 10000.1-f over \(\Q(\sqrt{-2}) \)

Isogeny class 10000.1-f contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
10000.1-f1	\( \bigl[a\) , \( 0\) , \( a\) , \( -12551\) , \( -539198\bigr] \)
10000.1-f2	\( \bigl[a\) , \( 0\) , \( a\) , \( -11\) , \( 22\bigr] \)
10000.1-f3	\( \bigl[a\) , \( 0\) , \( a\) , \( -51\) , \( -1698\bigr] \)
10000.1-f4	\( \bigl[a\) , \( 0\) , \( a\) , \( 89\) , \( -158\bigr] \)