Elliptic curve isogeny class 10.1-d over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-10.1-d
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-d over \(\Q(\sqrt{15}) \)

Isogeny class 10.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10.1-d1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 54 a - 205\) , \( 1800 a - 6965\bigr] \)
10.1-d2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 7454 a - 28865\) , \( 696920 a - 2699153\bigr] \)
10.1-d3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 119254 a - 461865\) , \( 44237360 a - 171330553\bigr] \)
10.1-d4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1474 a - 5705\) , \( 61924 a - 239825\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph