Elliptic curve isogeny class 30976.1-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-30976.1-d
• Conductor: 30976.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 30976.1-d over \(\Q(\sqrt{-2}) \)

Isogeny class 30976.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30976.1-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 7\) , \( 0\bigr] \)
30976.1-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 7\) , \( 0\bigr] \)
30976.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -66 a - 77\) , \( -350 a - 126\bigr] \)
30976.1-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -66 a - 77\) , \( 350 a + 126\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph