LMFDB - L-function search results

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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

Arithmetic

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Results (1-50 of 288 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4056-4056.1043-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1043	$0$	✓	✓	$0.100$	$0$	$0.899760$	Character $\chi_{4056}(1043, \cdot)$
1-4056-4056.1061-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1061	$0$	✓	✓	$0.202$	$0$	$0.801073$	Character $\chi_{4056}(1061, \cdot)$
1-4056-4056.1067-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1067	$0$	✓	✓	$-0.313$	$0$	$0.676253$	Character $\chi_{4056}(1067, \cdot)$
1-4056-4056.107-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.107	$0$	✓	✓	$-0.120$	$0$	$0.635160$	Character $\chi_{4056}(107, \cdot)$
1-4056-4056.1085-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1085	$0$	✓	✓	$-0.327$	$0$	$0.406711$	Character $\chi_{4056}(1085, \cdot)$
1-4056-4056.1091-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1091	$0$	✓	✓	$0.0473$	$0$	$0.747827$	Character $\chi_{4056}(1091, \cdot)$
1-4056-4056.1115-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1115	$0$	✓	✓	$0.0414$	$0$	$0.825399$	Character $\chi_{4056}(1115, \cdot)$
1-4056-4056.1133-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1133	$0$	✓	✓	$0.327$	$0$	$1.00903$	Character $\chi_{4056}(1133, \cdot)$
1-4056-4056.1181-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1181	$0$	✓	✓	$-0.399$	$0$	$1.53911$	Character $\chi_{4056}(1181, \cdot)$
1-4056-4056.1187-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1187	$0$	✓	✓	$-0.285$	$0$	$0.393378$	Character $\chi_{4056}(1187, \cdot)$
1-4056-4056.1229-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1229	$0$	✓	✓	$-0.399$	$0$	$0.255615$	Character $\chi_{4056}(1229, \cdot)$
1-4056-4056.125-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.125	$0$	✓	✓	$-0.399$	$0$	$0.380974$	Character $\chi_{4056}(125, \cdot)$
1-4056-4056.1283-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1283	$0$	✓	✓	$0.422$	$0$	$1.35401$	Character $\chi_{4056}(1283, \cdot)$
1-4056-4056.131-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.131	$0$	✓	✓	$0.100$	$0$	$0.649679$	Character $\chi_{4056}(131, \cdot)$
1-4056-4056.1355-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1355	$0$	✓	✓	$-0.244$	$0$	$0.168323$	Character $\chi_{4056}(1355, \cdot)$
1-4056-4056.1373-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1373	$0$	✓	✓	$0.313$	$0$	$0.790579$	Character $\chi_{4056}(1373, \cdot)$
1-4056-4056.1379-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1379	$0$	✓	✓	$-0.0414$	$0$	$0.579748$	Character $\chi_{4056}(1379, \cdot)$
1-4056-4056.1397-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1397	$0$	✓	✓	$0.480$	$0$	$0.0958531$	Character $\chi_{4056}(1397, \cdot)$
1-4056-4056.1403-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1403	$0$	✓	✓	$-0.186$	$0$	$0.589597$	Character $\chi_{4056}(1403, \cdot)$
1-4056-4056.1427-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1427	$0$	✓	✓	$0.399$	$0$	$1.43481$	Character $\chi_{4056}(1427, \cdot)$
1-4056-4056.1445-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1445	$0$	✓	✓	$0.130$	$0$	$0.625105$	Character $\chi_{4056}(1445, \cdot)$
1-4056-4056.149-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.149	$0$	✓	✓	$-0.130$	$0$	$0.588435$	Character $\chi_{4056}(149, \cdot)$
1-4056-4056.1493-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1493	$0$	✓	✓	$-0.208$	$0$	$0.325515$	Character $\chi_{4056}(1493, \cdot)$
1-4056-4056.1541-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1541	$0$	✓	✓	$-0.130$	$0$	$0.485523$	Character $\chi_{4056}(1541, \cdot)$
1-4056-4056.155-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.155	$0$	✓	✓	$0.286$	$0$	$1.07154$	Character $\chi_{4056}(155, \cdot)$
1-4056-4056.1565-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1565	$0$	✓	✓	$0.100$	$0$	$1.02740$	Character $\chi_{4056}(1565, \cdot)$
1-4056-4056.1595-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1595	$0$	✓	✓	$-0.453$	$0$	$0.444724$	Character $\chi_{4056}(1595, \cdot)$
1-4056-4056.1685-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1685	$0$	✓	✓	$-0.286$	$0$	$0.423847$	Character $\chi_{4056}(1685, \cdot)$
1-4056-4056.1715-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1715	$0$	✓	✓	$0.0414$	$0$	$0.854071$	Character $\chi_{4056}(1715, \cdot)$
1-4056-4056.1739-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1739	$0$	✓	✓	$-0.422$	$0$	$1.30850$	Character $\chi_{4056}(1739, \cdot)$
1-4056-4056.1757-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1757	$0$	✓	✓	$-0.464$	$0$	$1.47679$	Character $\chi_{4056}(1757, \cdot)$
1-4056-4056.179-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.179	$0$	✓	✓	$0.146$	$0$	$0.797264$	Character $\chi_{4056}(179, \cdot)$
1-4056-4056.1805-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1805	$0$	✓	✓	$0.379$	$0$	$1.19150$	Character $\chi_{4056}(1805, \cdot)$
1-4056-4056.1811-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1811	$0$	✓	✓	$-0.380$	$0$	$0.415066$	Character $\chi_{4056}(1811, \cdot)$
1-4056-4056.1853-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1853	$0$	✓	✓	$0.208$	$0$	$1.05696$	Character $\chi_{4056}(1853, \cdot)$
1-4056-4056.1877-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1877	$0$	✓	✓	$-0.202$	$0$	$0.284141$	Character $\chi_{4056}(1877, \cdot)$
1-4056-4056.1907-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1907	$0$	✓	✓	$-0.380$	$0$	$1.43298$	Character $\chi_{4056}(1907, \cdot)$
1-4056-4056.197-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.197	$0$	✓	✓	$-0.208$	$0$	$0.416748$	Character $\chi_{4056}(197, \cdot)$
1-4056-4056.1979-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1979	$0$	✓	✓	$-0.422$	$0$	$0.348973$	Character $\chi_{4056}(1979, \cdot)$
1-4056-4056.1997-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.1997	$0$	✓	✓	$0.208$	$0$	$1.14007$	Character $\chi_{4056}(1997, \cdot)$
1-4056-4056.2003-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2003	$0$	✓	✓	$0.0414$	$0$	$0.631976$	Character $\chi_{4056}(2003, \cdot)$
1-4056-4056.2021-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2021	$0$	✓	✓	$0.353$	$0$	$1.12902$	Character $\chi_{4056}(2021, \cdot)$
1-4056-4056.2069-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2069	$0$	✓	✓	$0.00542$	$0$	$0.836664$	Character $\chi_{4056}(2069, \cdot)$
1-4056-4056.2123-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2123	$0$	✓	✓	$0.0463$	$0$	$0.552869$	Character $\chi_{4056}(2123, \cdot)$
1-4056-4056.2165-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2165	$0$	✓	✓	$-0.208$	$0$	$0.744358$	Character $\chi_{4056}(2165, \cdot)$
1-4056-4056.2189-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2189	$0$	✓	✓	$-0.313$	$0$	$0.290269$	Character $\chi_{4056}(2189, \cdot)$
1-4056-4056.2291-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2291	$0$	✓	✓	$-0.100$	$0$	$0.472300$	Character $\chi_{4056}(2291, \cdot)$
1-4056-4056.2309-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2309	$0$	✓	✓	$0.338$	$0$	$1.04142$	Character $\chi_{4056}(2309, \cdot)$
1-4056-4056.2315-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2315	$0$	✓	✓	$0.313$	$0$	$1.48162$	Character $\chi_{4056}(2315, \cdot)$
1-4056-4056.2333-r0-0-0	$18.8$	$18.8$	$1$	$2^{3} \cdot 3 \cdot 13^{2}$	4056.2333	$0$	✓	✓	$-0.00542$	$0$	$0.566067$	Character $\chi_{4056}(2333, \cdot)$

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Elliptic curves over $\Q$
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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.