Elliptic curve isogeny class 19.1-b over number field \(\Q(\sqrt{35}) \)

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-19.1-b
• Conductor: 19.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 19.1-b over \(\Q(\sqrt{35}) \)

Isogeny class 19.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
19.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 13\) , \( -4 a + 24\bigr] \)
19.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -38 a - 53\) , \( -116 a - 1096\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph