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

• Base field: \(\Q(\sqrt{34}) \)
• Label: 2.2.136.1-18.1-c
• 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-c over \(\Q(\sqrt{34}) \)

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

Curve label	Weierstrass Coefficients
18.1-c1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -575 a - 3311\) , \( -24050 a - 140165\bigr] \)
18.1-c2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -3710 a - 21591\) , \( 2114774 a + 12331215\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph