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 (4 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
600.1-a3	600.1-a	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	600.1	\( 2^{3} \cdot 3 \cdot 5^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \)	$1.53203$	$(a+1), (a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \)	$0.222905284$	$3.910645665$	2.013113201	\( \frac{136835858}{1875} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -138 a - 239\) , \( -1187 a - 2059\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-138a-239\right){x}-1187a-2059$
600.1-d3	600.1-d	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	600.1	\( 2^{3} \cdot 3 \cdot 5^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \)	$1.53203$	$(a+1), (a), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \)	$0.374384071$	$12.39841016$	2.679925586	\( \frac{136835858}{1875} \)	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -136 a - 238\) , \( 1050 a + 1820\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-136a-238\right){x}+1050a+1820$
3600.1-a3	3600.1-a	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3600.1	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{10} \cdot 3^{8} \cdot 5^{8} \)	$2.39775$	$(a+1), (a), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$4.020190251$	2.321057923	\( \frac{136835858}{1875} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -102\) , \( -210 a\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-102{x}-210a$
3600.1-f3	3600.1-f	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3600.1	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{10} \cdot 3^{8} \cdot 5^{8} \)	$2.39775$	$(a+1), (a), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$4.020190251$	2.321057923	\( \frac{136835858}{1875} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -102\) , \( 210 a\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}-102{x}+210a$

 

  *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.