Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-507.1-c
Conductor 507.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 507.1-c over \(\Q(\sqrt{6}) \)

Isogeny class 507.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
507.1-c1 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 10 a + 26\) , \( 67 a + 164\bigr] \)
507.1-c2 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -90 a - 219\) , \( 512 a + 1254\bigr] \)
507.1-c3 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -390 a - 954\) , \( -6469 a - 15846\bigr] \)
507.1-c4 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1390 a - 3404\) , \( 42333 a + 103694\bigr] \)

Rank

Rank: \( 1 \)

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