Elliptic curve isogeny class 31212.7-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-31212.7-c
• Conductor: 31212.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 31212.7-c over \(\Q(\sqrt{-2}) \)

Isogeny class 31212.7-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
31212.7-c1	\( \bigl[a\) , \( -a\) , \( a\) , \( -535 a + 1193\) , \( -9864 a - 15891\bigr] \)
31212.7-c2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 4 a + 1412\) , \( 13982 a - 346\bigr] \)
31212.7-c3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -112 a + 25\) , \( 259 a - 730\bigr] \)
31212.7-c4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 84 a + 105\) , \( 141 a - 672\bigr] \)
31212.7-c5	\( \bigl[a\) , \( -a\) , \( 0\) , \( 9 a + 87\) , \( 200 a + 80\bigr] \)
31212.7-c6	\( \bigl[a\) , \( -a\) , \( a\) , \( -40 a + 68\) , \( -216 a - 222\bigr] \)
31212.7-c7	\( \bigl[a\) , \( -a\) , \( a\) , \( 255 a - 77\) , \( -1240 a - 1967\bigr] \)
31212.7-c8	\( \bigl[a\) , \( -a\) , \( 0\) , \( -186 a - 258\) , \( 2066 a - 220\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\ 12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\ 4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\ 12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\ 6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\ 2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\ 4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\ 3 & 4 & 12 & 4 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph