Elliptic curve isogeny class 1250.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1250.1-c
• Conductor: 1250.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1250.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 1250.1-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
1250.1-c1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
1250.1-c2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4228 a - 7325\) , \( -232635 a + 402935\bigr] \)
1250.1-c3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
1250.1-c4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -30772 a + 53300\) , \( 1717365 a - 2974565\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph