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 (5 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
225.1-a8	225.1-a	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	225.1	\( 3^{2} \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \)	$0.91566$	$(3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$0.689178076$	$0.558925428$	0.582366377	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
2025.1-a8	2025.1-a	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{20} \cdot 5^{2} \)	$1.58597$	$(3), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$16$	\( 2^{2} \)	$1$	$0.186308476$	2.253375518	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-19440{x}+1048135$
5625.1-b8	5625.1-b	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	5625.1	\( 3^{2} \cdot 5^{4} \)	\( 3^{8} \cdot 5^{14} \)	$2.04747$	$(3), (5)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	\( 2^{4} \)	$1$	$0.111785085$	1.352025311	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$
14400.1-d8	14400.1-d	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	14400.1	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{18} \cdot 3^{8} \cdot 5^{2} \)	$2.58987$	$(a), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$15.27600809$	$0.197609980$	4.563832806	\( \frac{1114544804970241}{405} \)	\( \bigl[a\) , \( a\) , \( 0\) , \( -10800 a - 4321\) , \( -661377 a + 241559\bigr] \)	${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10800a-4321\right){x}-661377a+241559$
14400.7-d8	14400.7-d	$8$	$16$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	14400.7	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{18} \cdot 3^{8} \cdot 5^{2} \)	$2.58987$	$(-a+1), (3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$15.27600809$	$0.197609980$	4.563832806	\( \frac{1114544804970241}{405} \)	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10802 a - 15122\) , \( 657057 a - 441419\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10802a-15122\right){x}+657057a-441419$

 

  *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.