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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-10.1-b
• 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-b over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -402 a + 1564\) , \( 14377 a - 55675\bigr] \)
10.1-b2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 188 a - 721\) , \( 2661 a - 10299\bigr] \)
10.1-b3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2983 a - 11546\) , \( 173253 a - 670999\bigr] \)
10.1-b4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 3148 a - 12186\) , \( 152797 a - 591775\bigr] \)

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