Properties

Base field \(\Q(\sqrt{30}) \)
Label 2.2.120.1-30.1-a
Conductor 30.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{30}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 30 \); class number \(2\).

Elliptic curves in class 30.1-a over \(\Q(\sqrt{30}) \)

Isogeny class 30.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
30.1-a1 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2384 a - 13010\) , \( -483140 a + 2646330\bigr] \)
30.1-a2 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -256 a + 1450\) , \( 16348 a - 89478\bigr] \)
30.1-a3 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 79824 a - 437170\) , \( -3882820 a + 21267130\bigr] \)
30.1-a4 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 12064 a - 66030\) , \( -1449060 a + 7936890\bigr] \)
30.1-a5 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3264 a - 17830\) , \( 215900 a - 1182470\bigr] \)
30.1-a6 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 58704 a - 321490\) , \( -18063172 a + 98936122\bigr] \)
30.1-a7 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 50784 a - 278110\) , \( 14594588 a - 79937798\bigr] \)
30.1-a8 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 938704 a - 5141490\) , \( -1158287172 a + 6344200122\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph