⌂ → Genus 2 curves → $\Q$ → 6075 → a → 18225

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Genus 2 curves in isogeny class 6075.a of discriminant 18225

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Conductor	Absolute discriminant	Rational points*	Weierstrass points	Torsion order

Bad \(p\)	2-Selmer rank	Analytic rank*	Analytic Ш*	Torsion

\(\Q\)-end algebra	\(\mathrm{ST}(X)\)	\(\mathrm{Aut}(X)\)	Square Ш*	\(\overline{\Q}\)-simple

\(\overline{\Q}\)-end algebra	\(\mathrm{ST}^0(X)\)	\(\mathrm{Aut}(X_{\overline{\Q}})\)	Locally solvable	$\GL_2$-type

Galois image	Nonmax$\ \ell$

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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
6075.a.18225.1	6075.a	\( 3^{5} \cdot 5^{2} \)	\( 3^{6} \cdot 5^{2} \)	$0$	$1$	$\Z/6\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_6)$		✓		$C_2$	$D_6$	$3$	$1$	2.120.1, 3.2880.4	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(15.574664\)	\(0.865259\)	$[164,2745,106365,-9600]$	$[123,-399,-409,-52377,-18225]$	$[-\frac{115856201}{75},\frac{9166493}{225},\frac{687529}{2025}]$	$y^2 + (x^3 + 1)y = x^3 + 1$

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