Elliptic curve search results

Results (9 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
121.2-a1	121.2-a	$3$	$25$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 11^{2} \)	$1.29185$	$(a+2), (a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.2	$1$	\( 1 \)	$5.612837583$	$0.370308724$	1.907346561	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)	${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.2-b1	121.2-b	$3$	$25$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 5^{12} \cdot 11^{2} \)	$2.88866$	$(11,a+4), (11,a+6)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.3	$25$	\( 1 \)	$5.612837583$	$0.370308724$	21.32478283	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -195508\) , \( -33338481\bigr] \)	${y}^2+{y}={x}^3+{x}^2-195508{x}-33338481$
11.1-d1	11.1-d	$3$	$25$	\(\Q(\sqrt{-627}) \)	$2$	$[0, 1]$	11.1	\( 11 \)	\( 11^{2} \cdot 13^{12} \)	$4.07493$	$(11,a+5)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.4.1	$1$	\( 2 \)	$42.97049067$	$0.370308724$	10.16764722	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 54742 a + 1102615\) , \( -31574829 a + 439435741\bigr] \)	${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(54742a+1102615\right){x}-31574829a+439435741$
11.1-d1	11.1-d	$3$	$25$	\(\Q(\sqrt{-209}) \)	$2$	$[0, 1]$	11.1	\( 11 \)	\( 11^{14} \)	$4.70533$	$(11,a)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.4.1	$1$	\( 2 \)	$123.8994719$	$0.740617449$	25.38927173	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( -946260\) , \( -354609587\bigr] \)	${y}^2+a{y}={x}^3+{x}^2-946260{x}-354609587$
11.1-d1	11.1-d	$3$	$25$	\(\Q(\sqrt{-1463}) \)	$2$	$[0, 1]$	11.1	\( 11 \)	\( 11^{2} \cdot 19^{12} \)	$6.22456$	$(11,a+5)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.4.1	$1$	\( 2 \)	$395.7942036$	$0.740617449$	61.30998272	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -2823140\) , \( 1824832093\bigr] \)	${y}^2+{y}={x}^3+{x}^2-2823140{x}+1824832093$
11.1-c1	11.1-c	$3$	$25$	\(\Q(\sqrt{-418}) \)	$2$	$[0, 1]$	11.1	\( 11 \)	\( 11^{2} \cdot 19^{12} \)	$6.65434$	$(11,a)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.4.1	$1$	\( 2 \)	$150.2059778$	$0.740617449$	21.76471614	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -2823140\) , \( 1824832093\bigr] \)	${y}^2+{y}={x}^3+{x}^2-2823140{x}+1824832093$
121.1-a1	121.1-a	$3$	$25$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{2} \)	$2.23755$	$(11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.4.2	$1$	\( 1 \)	$5.612837583$	$8.512583687$	12.65716488	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -94469627 a - 309380202\) , \( 970977133866 a + 3179869733625\bigr] \)	${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-94469627a-309380202\right){x}+970977133866a+3179869733625$
121.1-c1	121.1-c	$3$	$25$	\(\Q(\sqrt{19}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{2} \)	$2.58370$	$(11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.4.2	$1$	\( 1 \)	$5.612837583$	$8.512583687$	10.96142633	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( -7820\) , \( 263575\bigr] \)	${y}^2+a{y}={x}^{3}+{x}^{2}-7820{x}+263575$
11.1-b1	11.1-b	$3$	$25$	\(\Q(\sqrt{209}) \)	$2$	$[2, 0]$	11.1	\( 11 \)	\( 11^{2} \)	$2.35266$	$(70a+471)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.4.2	$1$	\( 2 \)	$5.612837583$	$8.512583687$	13.21997756	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4688891060561 a - 36237701385816\) , \( -14859019779017908422 a + 114836688394705117771\bigr] \)	${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4688891060561a-36237701385816\right){x}-14859019779017908422a+114836688394705117771$

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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.