Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-72.1-c
Conductor 72.1
Rank not recorded

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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-c over \(\Q(\sqrt{7}) \)

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

Curve label Weierstrass Coefficients
72.1-c1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 190 a + 504\) , \( -16334 a - 43216\bigr] \)
72.1-c2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-c3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -50 a - 131\) , \( 146 a + 386\bigr] \)
72.1-c4 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 293 a - 770\) , \( 4024 a - 10642\bigr] \)
72.1-c5 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 773 a - 2040\) , \( -19496 a + 51586\bigr] \)
72.1-c6 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4610 a - 12196\) , \( -286494 a - 757992\bigr] \)

Rank

Rank not yet determined.

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