Elliptic curve isogeny class 15.1-d over number field \(\Q(\sqrt{30}) \)

• Base field: \(\Q(\sqrt{30}) \)
• Label: 2.2.120.1-15.1-d
• Conductor: 15.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 15.1-d over \(\Q(\sqrt{30}) \)

Isogeny class 15.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
15.1-d1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
15.1-d2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
15.1-d3	\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
15.1-d4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
15.1-d5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
15.1-d6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
15.1-d7	\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
15.1-d8	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph