Elliptic curve isogeny class 44217.7-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-44217.7-c
• Conductor: 44217.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 44217.7-c over \(\Q(\sqrt{-2}) \)

Isogeny class 44217.7-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
44217.7-c1	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -712 a - 60\) , \( -6669 a + 7446\bigr] \)
44217.7-c2	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 8 a\) , \( -39 a + 51\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph