Elliptic curve isogeny class 6.2-a over number field \(\Q(\sqrt{46}) \)

• Base field: \(\Q(\sqrt{46}) \)
• Label: 2.2.184.1-6.2-a
• Conductor: 6.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{46}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 46 \); class number \(1\).

Elliptic curves in class 6.2-a over \(\Q(\sqrt{46}) \)

Isogeny class 6.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
6.2-a1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -187 a - 1189\) , \( -9426 a - 63802\bigr] \)
6.2-a2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4047 a - 27369\) , \( -375214 a - 2544698\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph