Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-72.1-d
Conductor 72.1
Rank \( 0 \)

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

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

Elliptic curves in class 72.1-d over \(\Q(\sqrt{7}) \)

Isogeny class 72.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
72.1-d1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 503\) , \( 17022 a + 45035\bigr] \)
72.1-d2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-d3 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -51 a - 132\) , \( -333 a - 882\bigr] \)
72.1-d4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 292 a - 771\) , \( -4503 a + 11915\bigr] \)
72.1-d5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 772 a - 2041\) , \( 18227 a - 48223\bigr] \)
72.1-d6 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4611 a - 12197\) , \( 269682 a + 713511\bigr] \)

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