Elliptic curve isogeny class 4.1-b over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-4.1-b
• Conductor: 4.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{85}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).

Elliptic curves in class 4.1-b over \(\Q(\sqrt{85}) \)

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -490 a - 2009\) , \( -14487 a - 59538\bigr] \)
4.1-b2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5 a + 26\) , \( 7 a + 30\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph