Elliptic curve isogeny class 15.1-d over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-15.1-d
• Conductor: 15.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 15.1-d over \(\Q(\sqrt{105}) \)

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

Curve label	Weierstrass Coefficients
15.1-d1	\( \bigl[a\) , \( -a\) , \( 0\) , \( -10235 a - 47290\) , \( 2386570 a + 11034280\bigr] \)
15.1-d2	\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a + 10\) , \( -540 a - 2460\bigr] \)
15.1-d3	\( \bigl[a\) , \( -a\) , \( 0\) , \( 3250 a + 15060\) , \( 124193 a + 574242\bigr] \)
15.1-d4	\( \bigl[a\) , \( -a\) , \( 0\) , \( -935 a - 4290\) , \( 15500 a + 71700\bigr] \)
15.1-d5	\( \bigl[a\) , \( -a\) , \( 0\) , \( -470 a - 2140\) , \( -12617 a - 58298\bigr] \)
15.1-d6	\( \bigl[a\) , \( -a\) , \( 0\) , \( -12560 a - 58040\) , \( 1723275 a + 7967550\bigr] \)
15.1-d7	\( \bigl[a\) , \( -a\) , \( 0\) , \( -7445 a - 34390\) , \( -796682 a - 3683408\bigr] \)
15.1-d8	\( \bigl[a\) , \( -a\) , \( 0\) , \( -200885 a - 928790\) , \( 110782080 a + 512198220\bigr] \)

Rank

Rank: \( 0 \)

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