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Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-90.1-e
Conductor 90.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 90.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 90.1-e contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
90.1-e1 \( \bigl[a\) , \( 1\) , \( a\) , \( 50600 a - 181335\) , \( 12006120 a - 39192277\bigr] \)
90.1-e2 \( \bigl[a\) , \( 1\) , \( a\) , \( -55\) , \( -565\bigr] \)
90.1-e3 \( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \)
90.1-e4 \( \bigl[a\) , \( 1\) , \( a\) , \( 740 a - 1875\) , \( 16212 a - 58945\bigr] \)
90.1-e5 \( \bigl[a\) , \( 1\) , \( a\) , \( -1815\) , \( -6165\bigr] \)
90.1-e6 \( \bigl[a\) , \( 1\) , \( a\) , \( -275\) , \( -1825\bigr] \)
90.1-e7 \( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( 135\bigr] \)
90.1-e8 \( \bigl[a\) , \( 1\) , \( a\) , \( -1335\) , \( -20277\bigr] \)
90.1-e9 \( \bigl[a\) , \( 1\) , \( a\) , \( -740 a - 1875\) , \( -16212 a - 58945\bigr] \)
90.1-e10 \( \bigl[a\) , \( 1\) , \( a\) , \( -1155\) , \( 13743\bigr] \)
90.1-e11 \( \bigl[a\) , \( 1\) , \( a\) , \( -21335\) , \( -1224277\bigr] \)
90.1-e12 \( \bigl[a\) , \( 1\) , \( a\) , \( -50600 a - 181335\) , \( -12006120 a - 39192277\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 8 & 24 & 3 & 8 & 6 & 12 & 4 & 12 & 24 & 2 & 4 \\ 8 & 1 & 3 & 24 & 4 & 12 & 6 & 2 & 24 & 12 & 4 & 8 \\ 24 & 3 & 1 & 8 & 12 & 4 & 2 & 6 & 8 & 4 & 12 & 24 \\ 3 & 24 & 8 & 1 & 24 & 2 & 4 & 12 & 4 & 8 & 6 & 12 \\ 8 & 4 & 12 & 24 & 1 & 12 & 6 & 2 & 24 & 3 & 4 & 8 \\ 6 & 12 & 4 & 2 & 12 & 1 & 2 & 6 & 2 & 4 & 3 & 6 \\ 12 & 6 & 2 & 4 & 6 & 2 & 1 & 3 & 4 & 2 & 6 & 12 \\ 4 & 2 & 6 & 12 & 2 & 6 & 3 & 1 & 12 & 6 & 2 & 4 \\ 12 & 24 & 8 & 4 & 24 & 2 & 4 & 12 & 1 & 8 & 6 & 3 \\ 24 & 12 & 4 & 8 & 3 & 4 & 2 & 6 & 8 & 1 & 12 & 24 \\ 2 & 4 & 12 & 6 & 4 & 3 & 6 & 2 & 6 & 12 & 1 & 2 \\ 4 & 8 & 24 & 12 & 8 & 6 & 12 & 4 & 3 & 24 & 2 & 1 \end{array}\right)\)

Isogeny graph