Elliptic curve isogeny class 12.2-a over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-12.2-a
• Conductor: 12.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 12.2-a over \(\Q(\sqrt{85}) \)

Isogeny class 12.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.2-a1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3749 a - 15408\) , \( 223496 a + 918518\bigr] \)
12.2-a2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -57679 a - 237048\) , \( 16063422 a + 66017006\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph