Elliptic curve isogeny class 30.1-b over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-30.1-b
• Conductor: 30.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 30.1-b over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
30.1-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
30.1-b2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
30.1-b3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
30.1-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
30.1-b5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
30.1-b6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
30.1-b7	\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
30.1-b8	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)

Rank

Rank: \( 1 \)

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