Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-98.1-i
Conductor 98.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 98.1-i over \(\Q(\sqrt{15}) \)

Isogeny class 98.1-i contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
98.1-i1 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 5454 a - 21143\) , \( 445825 a - 1726703\bigr] \)
98.1-i2 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 14 a - 63\) , \( -111 a + 425\bigr] \)
98.1-i3 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -146 a + 557\) , \( 2753 a - 10667\bigr] \)
98.1-i4 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 1134 a - 4403\) , \( 36289 a - 140555\bigr] \)
98.1-i5 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 334 a - 1303\) , \( -5839 a + 22609\bigr] \)
98.1-i6 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 87374 a - 338583\) , \( 27880833 a - 107983087\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph