Elliptic curve isogeny class 18.1-e over number field \(\Q(\sqrt{34}) \)

• Base field: \(\Q(\sqrt{34}) \)
• Label: 2.2.136.1-18.1-e
• Conductor: 18.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{34}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 34 \); class number \(2\).

Elliptic curves in class 18.1-e over \(\Q(\sqrt{34}) \)

Isogeny class 18.1-e contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
18.1-e1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 2\) , \( -7 a - 55\bigr] \)
18.1-e2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 12 a + 78\) , \( 13 a + 151\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph