Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{35}) \)

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-20.1-a
• Conductor: 20.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{35}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 35 \); class number \(2\).

Elliptic curves in class 20.1-a over \(\Q(\sqrt{35}) \)

Isogeny class 20.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 105 a - 633\) , \( 2716 a - 16072\bigr] \)
20.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -15 a + 77\) , \( -98 a + 576\bigr] \)
20.1-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( 64 a - 367\) , \( -591 a + 3504\bigr] \)
20.1-a4	\( \bigl[0\) , \( a\) , \( 0\) , \( 1984 a - 11727\) , \( 113073 a - 668944\bigr] \)

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