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

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-6.2-c
• Conductor: 6.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
6.2-c1	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -748 a - 3465\) , \( -20434 a - 94481\bigr] \)
6.2-c2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -22473 a - 103910\) , \( 4075678 a + 18843792\bigr] \)
6.2-c3	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -55698 a - 257525\) , \( -16381853 a - 75741099\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph