Genus 2 curves of conductor 5655

Results (displaying both 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
5655.a.84825.1	5655.a	\( 3 \cdot 5 \cdot 13 \cdot 29 \)	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 29 \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.180.3	✓	✓	$1$	\( 2^{2} \)	\(0.134007\)	\(13.339150\)	\(0.446884\)	$[18580,84985,530502093,10857600]$	$[4645,895460,229193056,65688283380,84825]$	$[86494518021956125/3393,3589742832979700/3393,197803004243296/3393]$	$y^2 + (x^2 + x + 1)y = -5x^5 - 17x^4 + x^3 + 6x^2 - 3x$
5655.b.491985.1	5655.b	\( 3 \cdot 5 \cdot 13 \cdot 29 \)	\( 3^{2} \cdot 5 \cdot 13 \cdot 29^{2} \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$4$	2.360.2	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(16.062150\)	\(1.003884\)	$[2340,104793,77140845,62974080]$	$[585,9893,101565,-9613981,491985]$	$[117117950625/841,3385631925/841,59415525/841]$	$y^2 + (x^2 + x)y = x^5 + 2x^4 - 4x^3 - 3x^2 + 3x$