Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-6272.7-b
Conductor 6272.7
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 6272.7-b over \(\Q(\sqrt{-7}) \)

Isogeny class 6272.7-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
6272.7-b1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -5969 a + 8354\) , \( -28195 a - 336690\bigr] \)
6272.7-b2 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 707 a - 93\) , \( -2681 a - 10093\bigr] \)
6272.7-b3 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 75 a - 1001\) , \( 1431 a - 12429\bigr] \)
6272.7-b4 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 40 a - 56\) , \( -144 a + 80\bigr] \)
6272.7-b5 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 42 a - 58\) , \( 154 a - 174\bigr] \)
6272.7-b6 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -19 a + 24\) , \( 15 a + 136\bigr] \)
6272.7-b7 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 156 a - 221\) , \( -265 a - 2608\bigr] \)
6272.7-b8 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1778 a - 198\) , \( -18676 a - 48180\bigr] \)
6272.7-b9 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 110 a + 2534\) , \( 6716 a - 65076\bigr] \)
6272.7-b10 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -1244 a + 1739\) , \( -1945 a - 25344\bigr] \)
6272.7-b11 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -369 a + 514\) , \( 575 a + 5624\bigr] \)
6272.7-b12 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -95569 a + 133794\) , \( -1891875 a - 21812018\bigr] \)

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