Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-432.2-c
Conductor 432.2
Rank \( 0 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 432.2-c over \(\Q(\sqrt{7}) \)

Isogeny class 432.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
432.2-c1 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 15 a + 40\) , \( 427 a + 1123\bigr] \)
432.2-c2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 38\) , \( -70 a + 185\bigr] \)
432.2-c3 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5 a - 15\) , \( -10 a - 27\bigr] \)
432.2-c4 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -25 a - 70\) , \( 85 a + 223\bigr] \)
432.2-c5 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -65 a - 180\) , \( -523 a - 1377\bigr] \)
432.2-c6 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -385 a - 1060\) , \( 6583 a + 17323\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph