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$\ \ell$

Sort order

Select

Results (6 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
75.1-a2	75.1-a	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{2} \cdot 5^{2} \)	$0.91095$	$(a), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2 \)	$1$	$10.19195692$	1.471082268	\( -\frac{1}{15} \)	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 227 a - 390\) , \( 392730 a - 680227\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(227a-390\right){x}+392730a-680227$
75.1-b2	75.1-b	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{2} \cdot 5^{2} \)	$0.91095$	$(a), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2 \)	$0.325078210$	$31.38702211$	0.736355203	\( -\frac{1}{15} \)	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 225 a - 391\) , \( -392504 a + 679835\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(225a-391\right){x}-392504a+679835$
1875.1-c2	1875.1-c	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1875.1	\( 3 \cdot 5^{4} \)	\( 3^{2} \cdot 5^{14} \)	$2.03695$	$(a), (5)$	$0$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	\( 2^{3} \)	$1$	$2.038391385$	1.176865815	\( -\frac{1}{15} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( -24\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-2{x}-24$
1875.1-d2	1875.1-d	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1875.1	\( 3 \cdot 5^{4} \)	\( 3^{2} \cdot 5^{14} \)	$2.03695$	$(a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$0.600243838$	$6.277404423$	4.350880830	\( -\frac{1}{15} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$
3600.1-d2	3600.1-d	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3600.1	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 5^{2} \)	$2.39775$	$(a+1), (a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$0.333082592$	$5.163131942$	3.971591054	\( -\frac{1}{15} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -a - 2\) , \( -5 a - 1\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-2\right){x}-5a-1$
3600.1-j2	3600.1-j	$8$	$16$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	3600.1	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 5^{2} \)	$2.39775$	$(a+1), (a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$0.333082592$	$5.163131942$	3.971591054	\( -\frac{1}{15} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 2\) , \( 4 a - 1\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+4a-1$

 

  *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.