Elliptic curve isogeny class 36.1-e over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-36.1-e
• Conductor: 36.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{42}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 42 \); class number \(2\).

Elliptic curves in class 36.1-e over \(\Q(\sqrt{42}) \)

Isogeny class 36.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.1-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -10800 a - 69992\bigr] \)
36.1-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 23622300 a + 153090001\bigr] \)
36.1-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -195 a - 1227\) , \( -4395 a - 28440\bigr] \)
36.1-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -525720 a - 3407055\) , \( 519690600 a + 3367980022\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph