Elliptic curve isogeny class 1458.3-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1458.3-b
• Conductor: 1458.3
• 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 1458.3-b over \(\Q(\sqrt{-2}) \)

Isogeny class 1458.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1458.3-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( a + 13\) , \( 28 a + 5\bigr] \)
1458.3-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 10\) , \( -10 a - 3\bigr] \)