Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 51.4-c over \(\Q(\sqrt{13}) \)
Isogeny class 51.4-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 51.4-c1 | \( \bigl[1\) , \( a\) , \( a\) , \( 5 a + 1\) , \( 2 a - 2\bigr] \) |
| 51.4-c2 | \( \bigl[1\) , \( a\) , \( a\) , \( 15 a - 84\) , \( 77 a - 275\bigr] \) |