Elliptic curve isogeny class 36.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-36.1-b
• Conductor: 36.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 36.1-b over \(\Q(\sqrt{7}) \)

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

Curve label	Weierstrass Coefficients
36.1-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4 a - 8\) , \( 16 a - 38\bigr] \)
36.1-b2	\( \bigl[0\) , \( a\) , \( 0\) , \( 64 a - 167\) , \( -431 a + 1141\bigr] \)
36.1-b3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \)
36.1-b4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6 a - 8\) , \( 6 a + 18\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph