Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-126.1-c
Conductor 126.1
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 126.1-c over \(\Q(\sqrt{7}) \)

Isogeny class 126.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
126.1-c1 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 170 a + 454\) , \( -1361 a - 3603\bigr] \)
126.1-c2 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -55 a - 141\) , \( -239 a - 635\bigr] \)
126.1-c3 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -25 a - 61\) , \( 87 a + 227\bigr] \)
126.1-c4 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -760 a - 2016\) , \( -19061 a - 50435\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph