Elliptic curve isogeny class 18513.5-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-18513.5-d
• Conductor: 18513.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 18513.5-d over \(\Q(\sqrt{-2}) \)

Isogeny class 18513.5-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
18513.5-d1	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 6 a - 21\) , \( -54 a + 25\bigr] \)
18513.5-d2	\( \bigl[a\) , \( a\) , \( 1\) , \( 9 a + 35\) , \( 56 a - 73\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph