Elliptic curve isogeny class 30492.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-c
• Conductor: 30492.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 30492.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30492.5-c1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -30 a - 6\) , \( -84 a + 28\bigr] \)
30492.5-c2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5 a - 4\) , \( -26 a + 32\bigr] \)
30492.5-c3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 25 a + 116\) , \( -398 a + 392\bigr] \)
30492.5-c4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 9 a - 61\) , \( -56 a + 164\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph