Elliptic curve isogeny class 3087.1-h over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3087.1-h
• Conductor: 3087.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3087.1-h over \(\Q(\sqrt{2}) \)

Isogeny class 3087.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3087.1-h1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 136 a - 306\) , \( -4774 a + 5425\bigr] \)
3087.1-h2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \)
3087.1-h3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16 a - 36\) , \( -22 a + 25\bigr] \)
3087.1-h4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 156 a - 351\) , \( 1980 a - 2250\bigr] \)
3087.1-h5	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 196 a - 441\) , \( -2992 a + 3400\bigr] \)
3087.1-h6	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 3136 a - 7056\) , \( -187330 a + 212875\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph