Elliptic curve isogeny class 6.2-b over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-6.2-b
• Conductor: 6.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6.2-b over \(\Q(\sqrt{105}) \)

Isogeny class 6.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
6.2-b1	\( \bigl[0\) , \( -a\) , \( a\) , \( -106 a - 483\) , \( 1156 a + 5343\bigr] \)
6.2-b2	\( \bigl[0\) , \( -a\) , \( a\) , \( -3186 a - 14723\) , \( -215575 a - 996707\bigr] \)
6.2-b3	\( \bigl[0\) , \( -a\) , \( a\) , \( -7896 a - 36503\) , \( 879389 a + 4065829\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph