Elliptic curve isogeny class 1458.6-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1458.6-a
• Conductor: 1458.6
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1458.6-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1458.6-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1458.6-a1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a - 3\) , \( 2\bigr] \)
1458.6-a2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -91 a - 48\) , \( -405 a + 128\bigr] \)