Elliptic curve isogeny class 19.2-a over number field \(\Q(\sqrt{35}) \)

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-19.2-a
• Conductor: 19.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 19.2-a over \(\Q(\sqrt{35}) \)

Isogeny class 19.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
19.2-a1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 12 a + 32\) , \( 24 a + 69\bigr] \)
19.2-a2	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 842 a - 4878\) , \( -31805 a + 188374\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph