Elliptic curve isogeny class 12.2-c over number field \(\Q(\sqrt{157}) \)

• Base field: \(\Q(\sqrt{157}) \)
• Label: 2.2.157.1-12.2-c
• Conductor: 12.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{157}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 39 \); class number \(1\).

Elliptic curves in class 12.2-c over \(\Q(\sqrt{157}) \)

Isogeny class 12.2-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
12.2-c1	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 4 a + 10\) , \( 2 a + 6\bigr] \)
12.2-c2	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -751 a - 4350\) , \( -32791 a - 189060\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph