Elliptic curve isogeny class 4356.4-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.4-c
• Conductor: 4356.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 4356.4-c over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.4-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4356.4-c1	\( \bigl[1\) , \( 1\) , \( a\) , \( 270 a - 724\) , \( 3957 a - 6986\bigr] \)
4356.4-c2	\( \bigl[1\) , \( a\) , \( 1\) , \( 257 a + 476\) , \( 4351 a - 1968\bigr] \)
4356.4-c3	\( \bigl[1\) , \( a\) , \( 1\) , \( -103 a - 84\) , \( 463 a - 272\bigr] \)
4356.4-c4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -262 a + 249\) , \( 591 a - 2832\bigr] \)

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