Elliptic curve isogeny class 27378.3-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27378.3-c
• Conductor: 27378.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 27378.3-c over \(\Q(\sqrt{-2}) \)

Isogeny class 27378.3-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27378.3-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4136\) , \( 103403\bigr] \)
27378.3-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -41\) , \( 209\bigr] \)
27378.3-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph