Elliptic curve isogeny class 375.1-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.1-c
• Conductor: 375.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 375.1-c over \(\Q(\sqrt{6}) \)

Isogeny class 375.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
375.1-c1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -357 a + 870\) , \( 178 a - 439\bigr] \)
375.1-c2	\( \bigl[a\) , \( 1\) , \( 1\) , \( -12 a - 44\) , \( -59 a - 163\bigr] \)
375.1-c3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 328 a - 812\) , \( -5101 a + 12497\bigr] \)
375.1-c4	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1242 a - 3040\) , \( 37208 a + 91141\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 10 & 5 \\ 2 & 1 & 5 & 10 \\ 10 & 5 & 1 & 2 \\ 5 & 10 & 2 & 1 \end{array}\right)\)

Isogeny graph