Elliptic curve isogeny class 6272.2-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6272.2-b
• Conductor: 6272.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6272.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 6272.2-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
6272.2-b1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 5967 a + 2388\) , \( 30581 a - 379207\bigr] \)
6272.2-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -75 a - 926\) , \( -1431 a - 10998\bigr] \)
6272.2-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( -705 a + 613\) , \( 3295 a - 11977\bigr] \)
6272.2-b4	\( \bigl[a\) , \( a\) , \( 0\) , \( -40 a - 17\) , \( -170 a + 77\bigr] \)
6272.2-b5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -40 a - 16\) , \( 144 a - 64\bigr] \)
6272.2-b6	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 17 a + 8\) , \( -9 a + 109\bigr] \)
6272.2-b7	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -158 a - 62\) , \( 201 a - 2495\bigr] \)
6272.2-b8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -110 a + 2644\) , \( -6716 a - 58360\bigr] \)
6272.2-b9	\( \bigl[a\) , \( a\) , \( 0\) , \( 1780 a - 1977\) , \( 16700 a - 68439\bigr] \)
6272.2-b10	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 1242 a + 498\) , \( 2441 a - 30271\bigr] \)
6272.2-b11	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 367 a + 148\) , \( -429 a + 5317\bigr] \)
6272.2-b12	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 95567 a + 38228\) , \( 1930101 a - 23933255\bigr] \)

Rank

Rank: \( 1 \)

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