Elliptic curve isogeny class 1568.2-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-1568.2-b
• Conductor: 1568.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 1568.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 1568.2-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
1568.2-b1	\( \bigl[a\) , \( -a\) , \( a\) , \( -3581 a + 2388\) , \( 55046 a - 134557\bigr] \)
1568.2-b2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 269 a + 194\) , \( 1017 a - 4482\bigr] \)
1568.2-b3	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 200 a - 507\) , \( 2267 a - 4120\bigr] \)
1568.2-b4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 25 a - 17\) , \( -36 a - 46\bigr] \)
1568.2-b5	\( \bigl[a\) , \( 0\) , \( 0\) , \( 24 a - 16\) , \( 44 a + 12\bigr] \)
1568.2-b6	\( \bigl[a\) , \( -a\) , \( a\) , \( -11 a + 8\) , \( -16 a + 39\bigr] \)
1568.2-b7	\( \bigl[a\) , \( -a\) , \( a\) , \( 94 a - 62\) , \( 362 a - 885\bigr] \)
1568.2-b8	\( \bigl[a\) , \( 0\) , \( 0\) , \( -606 a - 716\) , \( 5616 a - 23564\bigr] \)
1568.2-b9	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -395 a + 1383\) , \( 13026 a - 20402\bigr] \)
1568.2-b10	\( \bigl[a\) , \( -a\) , \( a\) , \( -746 a + 498\) , \( 4394 a - 10741\bigr] \)
1568.2-b11	\( \bigl[a\) , \( -a\) , \( a\) , \( -221 a + 148\) , \( -772 a + 1887\bigr] \)
1568.2-b12	\( \bigl[a\) , \( -a\) , \( a\) , \( -57341 a + 38228\) , \( 3474182 a - 8492445\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph