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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

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Results (31 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-504-168.83-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	168.83	$0.0$	✓	✓			$-0.0270$	$0$	$1.11445$	Modular form 504.1.e.a.251.1
2-504-168.83-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	168.83	$0.0$	✓	✓			$-0.222$	$0$	$1.56974$	Modular form 504.1.e.a.251.4
2-504-168.83-c0-0-2	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	168.83	$0.0$	✓	✓			$0.0270$	$0$	$1.84942$	Modular form 504.1.e.a.251.2
2-504-168.83-c0-0-3	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	168.83	$0.0$	✓	✓			$0.222$	$0$	$2.55031$	Modular form 504.1.e.a.251.3
2-504-21.11-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	21.11	$0.0$	✓	✓			$-0.171$	$0$	$1.08160$	Modular form 504.1.cu.a.305.1
2-504-21.11-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	21.11	$0.0$	✓	✓			$0.0247$	$0$	$1.96149$	Modular form 504.1.cu.a.305.2
2-504-21.2-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	21.2	$0.0$	✓	✓			$-0.0247$	$0$	$1.82436$	Modular form 504.1.cu.a.233.2
2-504-21.2-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	21.2	$0.0$	✓	✓			$0.171$	$0$	$2.13280$	Modular form 504.1.cu.a.233.1
2-504-504.13-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.13	$0.0$	✓	✓			$-0.277$	$0$	$1.12822$	Modular form 504.1.bn.c.13.1
2-504-504.13-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.13	$0.0$	✓	✓			$0.222$	$0$	$1.38591$	Modular form 504.1.bn.a.13.1
2-504-504.13-c0-0-2	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.13	$0.0$	✓	✓			$-0.277$	$0$	$1.70101$	Modular form 504.1.bn.c.13.2
2-504-504.13-c0-0-3	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.13	$0.0$	✓	✓			$0.222$	$0$	$2.24204$	Artin representation 2.504.6t5.b.a Modular form 504.1.bn.b.13.1
2-504-504.331-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.331	$0.0$	✓	✓			$0.184$	$0$	$2.52439$	Modular form 504.1.ba.a.331.1
2-504-504.331-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.331	$0.0$	✓	✓			$0.184$	$0$	$2.65695$	Modular form 504.1.ba.a.331.2
2-504-504.349-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.349	$0.0$	✓	✓			$-0.222$	$0$	$0.881950$	Modular form 504.1.bn.a.349.1
2-504-504.349-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.349	$0.0$	✓	✓			$-0.222$	$0$	$1.55295$	Artin representation 2.504.6t5.b.b Modular form 504.1.bn.b.349.1
2-504-504.349-c0-0-2	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.349	$0.0$	✓	✓			$0.277$	$0$	$2.43267$	Modular form 504.1.bn.c.349.1
2-504-504.349-c0-0-3	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.349	$0.0$	✓	✓			$0.277$	$0$	$2.61924$	Modular form 504.1.bn.c.349.2
2-504-504.403-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.403	$0.0$	✓	✓			$0.0378$	$0$	$1.11802$	Modular form 504.1.ce.a.403.1
2-504-504.403-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.403	$0.0$	✓	✓			$0.0378$	$0$	$1.66288$	Modular form 504.1.ce.a.403.2
2-504-504.499-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.499	$0.0$	✓	✓			$-0.0378$	$0$	$0.765881$	Modular form 504.1.ce.a.499.1
2-504-504.499-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.499	$0.0$	✓	✓			$-0.0378$	$0$	$1.78811$	Modular form 504.1.ce.a.499.2
2-504-504.67-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.67	$0.0$	✓	✓			$-0.184$	$0$	$1.20648$	Modular form 504.1.ba.a.67.1
2-504-504.67-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	504.67	$0.0$	✓	✓			$-0.184$	$0$	$1.95492$	Modular form 504.1.ba.a.67.2
2-504-56.13-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.13	$0.0$	✓	✓			$-0.250$	$0$	$1.34936$	Artin representation 2.504.8t11.a.a Modular form 504.1.l.b.181.2
2-504-56.13-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.13	$0.0$	✓	✓			$0.250$	$0$	$1.98369$	Artin representation 2.504.8t11.a.b Modular form 504.1.l.b.181.1
2-504-56.13-c0-0-2	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.13	$0.0$	✓	✓	✓	✓	$0$	$0$	$2.15848$	Artin representation 2.504.4t3.a Artin representation 2.504.4t3.a.a Modular form 504.1.l.a Modular form 504.1.l.a.181.1
2-504-56.45-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.45	$0.0$	✓	✓			$-0.270$	$0$	$1.08449$	Modular form 504.1.bw.a.325.1
2-504-56.45-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.45	$0.0$	✓	✓			$0.229$	$0$	$2.79665$	Modular form 504.1.bw.a.325.2
2-504-56.5-c0-0-0	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.5	$0.0$	✓	✓			$-0.229$	$0$	$1.45716$	Modular form 504.1.bw.a.397.2
2-504-56.5-c0-0-1	$0.501$	$0.251$	$2$	$2^{3} \cdot 3^{2} \cdot 7$	56.5	$0.0$	✓	✓			$0.270$	$0$	$2.26243$	Modular form 504.1.bw.a.397.1

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.