Elliptic curve isogeny class 1458.1-z over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1458.1-z
• Conductor: 1458.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1458.1-z over \(\Q(\sqrt{2}) \)

Isogeny class 1458.1-z contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1458.1-z1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 5\) , \( 5 a + 7\bigr] \)
1458.1-z2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 a + 25\) , \( -27 a - 53\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph