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
4225.2-a1	4225.2-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	4225.2	\( 5^{2} \cdot 13^{2} \)	\( 5^{4} \cdot 13^{4} \)	$1.24783$	$(-4a+1), (4a-3), (5)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$0.038447381$	$3.421514516$	1.215190886	\( \frac{6967871}{4225} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \)	${y}^2+{x}{y}={x}^{3}+4{x}+1$
54925.2-a1	54925.2-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	54925.2	\( 5^{2} \cdot 13^{3} \)	\( 5^{4} \cdot 13^{10} \)	$2.36942$	$(-4a+1), (4a-3), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$0.948957386$	4.383046421	\( \frac{6967871}{4225} \)	\( \bigl[1\) , \( -a\) , \( 0\) , \( 32 a - 60\) , \( 36 a + 17\bigr] \)	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(32a-60\right){x}+36a+17$
54925.3-a1	54925.3-a	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	54925.3	\( 5^{2} \cdot 13^{3} \)	\( 5^{4} \cdot 13^{10} \)	$2.36942$	$(-4a+1), (4a-3), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$0.948957386$	4.383046421	\( \frac{6967871}{4225} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -28 a + 60\) , \( -36 a + 53\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a+60\right){x}-36a+53$
105625.2-e1	105625.2-e	$2$	$2$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	105625.2	\( 5^{4} \cdot 13^{2} \)	\( 5^{16} \cdot 13^{4} \)	$2.79024$	$(-4a+1), (4a-3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \)	$0.908981164$	$0.684302903$	5.745960314	\( \frac{6967871}{4225} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -100 a\) , \( 125\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-100a{x}+125$

 

  *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.