Elliptic curve isogeny class 6.1-d over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-6.1-d
• Conductor: 6.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 6.1-d over \(\Q(\sqrt{105}) \)

Isogeny class 6.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
6.1-d1	\( \bigl[a\) , \( -a\) , \( a\) , \( 929 a - 5265\) , \( -32129 a + 180702\bigr] \)
6.1-d2	\( \bigl[a\) , \( -a\) , \( a\) , \( 9 a - 65\) , \( -a - 2\bigr] \)
6.1-d3	\( \bigl[a\) , \( -a\) , \( a\) , \( 374 a - 2115\) , \( 10279 a - 57810\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph