Elliptic curve search results

Results (13 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
75.1-a5	75.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	75.1	$3 \cdot 5^{2}$	$3^{4} \cdot 5^{4}$	$0.45547$	$(-2a+1), (5)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{2}$	$1$	$4.471403425$	0.322695746	$\frac{13997521}{225}$	$\bigl[1$ , $1$ , $1$ , $-5$ , $2\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
1875.1-b5	1875.1-b	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	1875.1	$3 \cdot 5^{4}$	$3^{4} \cdot 5^{16}$	$1.01847$	$(-2a+1), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$0.894280685$	1.032626388	$\frac{13997521}{225}$	$\bigl[1$ , $0$ , $1$ , $-126$ , $523\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$
11025.1-c5	11025.1-c	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	11025.1	$3^{2} \cdot 5^{2} \cdot 7^{2}$	$3^{10} \cdot 5^{4} \cdot 7^{6}$	$1.58597$	$(-2a+1), (-3a+1), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$0.975740221$	2.253375518	$\frac{13997521}{225}$	$\bigl[a + 1$ , $-a - 1$ , $1$ , $75 a + 45$ , $221 a - 483\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(75a+45\right){x}+221a-483$
11025.3-c5	11025.3-c	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	11025.3	$3^{2} \cdot 5^{2} \cdot 7^{2}$	$3^{10} \cdot 5^{4} \cdot 7^{6}$	$1.58597$	$(-2a+1), (3a-2), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$0.975740221$	2.253375518	$\frac{13997521}{225}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $-43 a - 76$ , $-341 a - 217\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-76\right){x}-341a-217$
12675.1-a5	12675.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	12675.1	$3 \cdot 5^{2} \cdot 13^{2}$	$3^{4} \cdot 5^{4} \cdot 13^{6}$	$1.64224$	$(-2a+1), (-4a+1), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$1.240144178$	2.863990301	$\frac{13997521}{225}$	$\bigl[1$ , $a + 1$ , $1$ , $-39 a + 75$ , $149 a + 117\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-39a+75\right){x}+149a+117$
12675.3-a5	12675.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	12675.3	$3 \cdot 5^{2} \cdot 13^{2}$	$3^{4} \cdot 5^{4} \cdot 13^{6}$	$1.64224$	$(-2a+1), (4a-3), (5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1$	$1.240144178$	2.863990301	$\frac{13997521}{225}$	$\bigl[a$ , $-a - 1$ , $a$ , $-75 a + 41$ , $-114 a + 191\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-75a+41\right){x}-114a+191$
19200.1-g5	19200.1-g	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	19200.1	$2^{8} \cdot 3 \cdot 5^{2}$	$2^{24} \cdot 3^{4} \cdot 5^{4}$	$1.82190$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.650156421$	$1.117850856$	3.356843389	$\frac{13997521}{225}$	$\bigl[0$ , $1$ , $0$ , $-80$ , $-300\bigr]$	${y}^2={x}^{3}+{x}^{2}-80{x}-300$
57600.1-j5	57600.1-j	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	57600.1	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{24} \cdot 3^{10} \cdot 5^{4}$	$2.39775$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1.332330370$	$0.645391492$	3.971591054	$\frac{13997521}{225}$	$\bigl[0$ , $-a - 1$ , $0$ , $-240 a$ , $1800 a - 900\bigr]$	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-240a{x}+1800a-900$
57600.1-k5	57600.1-k	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	57600.1	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{24} \cdot 3^{10} \cdot 5^{4}$	$2.39775$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1.332330370$	$0.645391492$	3.971591054	$\frac{13997521}{225}$	$\bigl[0$ , $a + 1$ , $0$ , $242 a - 241$ , $-1559 a + 659\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(242a-241\right){x}-1559a+659$
81225.1-a5	81225.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	81225.1	$3^{2} \cdot 5^{2} \cdot 19^{2}$	$3^{10} \cdot 5^{4} \cdot 19^{6}$	$2.61289$	$(-2a+1), (-5a+3), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1.006926864$	$0.592251851$	2.754442525	$\frac{13997521}{225}$	$\bigl[a$ , $a$ , $a + 1$ , $-76 a - 241$ , $591 a + 1422\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-76a-241\right){x}+591a+1422$
81225.3-a5	81225.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	81225.3	$3^{2} \cdot 5^{2} \cdot 19^{2}$	$3^{10} \cdot 5^{4} \cdot 19^{6}$	$2.61289$	$(-2a+1), (-5a+2), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{5}$	$1.006926864$	$0.592251851$	2.754442525	$\frac{13997521}{225}$	$\bigl[1$ , $a$ , $a$ , $241 a + 75$ , $-592 a + 2014\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(241a+75\right){x}-592a+2014$
102675.1-a5	102675.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	102675.1	$3 \cdot 5^{2} \cdot 37^{2}$	$3^{4} \cdot 5^{4} \cdot 37^{6}$	$2.77055$	$(-2a+1), (-7a+4), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$3.018158676$	$0.735094194$	5.123708641	$\frac{13997521}{225}$	$\bigl[a + 1$ , $-a + 1$ , $0$ , $35 a + 166$ , $-1081 a + 831\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(35a+166\right){x}-1081a+831$
102675.3-a5	102675.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	102675.3	$3 \cdot 5^{2} \cdot 37^{2}$	$3^{4} \cdot 5^{4} \cdot 37^{6}$	$2.77055$	$(-2a+1), (-7a+3), (5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	$2^{4}$	$3.018158676$	$0.735094194$	5.123708641	$\frac{13997521}{225}$	$\bigl[1$ , $-a$ , $0$ , $201 a - 166$ , $1081 a - 250\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(201a-166\right){x}+1081a-250$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.