Genus 2 curve search results

Results (4 matches)

 

Label	Class	Conductor	Discriminant	Rank*	2-Selmer rank	Torsion	$\textrm{End}^0(J_{\overline\Q})$	$\textrm{End}^0(J)$	$\GL_2\textsf{-type}$	Sato-Tate	Nonmaximal primes	$\Q$-simple	\(\overline{\Q}\)-simple	\(\Aut(X)\)	\(\Aut(X_{\overline{\Q}})\)	$\Q$-points	$\Q$-Weierstrass points	mod-$\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
1408.b.720896.2	1408.b	\( 2^{7} \cdot 11 \)	\( - 2^{16} \cdot 11 \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(7.656364\)	\(0.478523\)	$[32,-80,-1240,-88]$	$[128,1536,45056,851968,-720896]$	$[-524288/11,-49152/11,-1024]$	$y^2 = x^5 + 2x^3 - 4x^2 + x$
2816.a.720896.1	2816.a	\( 2^{8} \cdot 11 \)	\( - 2^{16} \cdot 11 \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(11.788192\)	\(0.736762\)	$[32,-80,-1240,-88]$	$[128,1536,45056,851968,-720896]$	$[-524288/11,-49152/11,-1024]$	$y^2 = x^5 + 2x^3 + 4x^2 + x$
45056.c.720896.1	45056.c	\( 2^{12} \cdot 11 \)	\( - 2^{16} \cdot 11 \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(7.656364\)	\(1.914091\)	$[32,-80,-1240,-88]$	$[128,1536,45056,851968,-720896]$	$[-524288/11,-49152/11,-1024]$	$y^2 = x^5 + x^4 - 2x^3 + x - 1$
45056.f.720896.1	45056.f	\( 2^{12} \cdot 11 \)	\( - 2^{16} \cdot 11 \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(0.576143\)	\(11.788192\)	\(1.697921\)	$[32,-80,-1240,-88]$	$[128,1536,45056,851968,-720896]$	$[-524288/11,-49152/11,-1024]$	$y^2 = x^5 - x^4 - 2x^3 + x + 1$