Elliptic curve isogeny class 7500.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-7500.1-c
• Conductor: 7500.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 7500.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 7500.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
7500.1-c1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
7500.1-c2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \)
7500.1-c3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \)
7500.1-c4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph