Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Results (7 matches)

 

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
1600.4-a3	1600.4-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	1600.4	\( 2^{6} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{2} \)	$1.49526$	$(a), (-a+1), (5)$	$0$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1$	$5.993777963$	1.132717564	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)	${y}^2={x}^{3}-2{x}+1$
6400.5-b3	6400.5-b	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	6400.5	\( 2^{8} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{2} \)	$2.11462$	$(a), (-a+1), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 1 \)	$1$	$5.993777963$	1.132717564	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2={x}^{3}-2{x}-1$
12800.4-g3	12800.4-g	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	12800.4	\( 2^{9} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$2.51472$	$(a), (-a+1), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$1$	$4.238241043$	3.203809084	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( a + 2\bigr] \)	${y}^2={x}^{3}+\left(-2a+4\right){x}+a+2$
12800.7-g3	12800.7-g	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	12800.7	\( 2^{9} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$2.51472$	$(a), (-a+1), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$1$	$4.238241043$	3.203809084	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( -a + 3\bigr] \)	${y}^2={x}^{3}+\left(2a+2\right){x}-a+3$
25600.5-c3	25600.5-c	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	25600.5	\( 2^{10} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$2.99053$	$(a), (-a+1), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$4.238241043$	1.601904542	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( -a - 2\bigr] \)	${y}^2={x}^{3}+\left(-2a+4\right){x}-a-2$
25600.7-c3	25600.7-c	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	25600.7	\( 2^{10} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$2.99053$	$(a), (-a+1), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$4.238241043$	1.601904542	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( a - 3\bigr] \)	${y}^2={x}^{3}+\left(2a+2\right){x}+a-3$
40000.4-e3	40000.4-e	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	40000.4	\( 2^{6} \cdot 5^{4} \)	\( 2^{8} \cdot 5^{14} \)	$3.34351$	$(a), (-a+1), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \)	$3.156731320$	$1.198755592$	5.721096022	\( \frac{55296}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \)	${y}^2={x}^{3}-50{x}+125$

 

  *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.