Elliptic curves over $\Q$ of conductor 26

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
26.a1	26a2	26.a	26a	$3$	$9$	\( 2 \cdot 13 \)	\( - 2^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.3	3B.1.2	$1$	$1$		$0$	$6$	$0.054386$	$-10730978619193/6656$	$[1, 0, 1, -460, -3830]$	\(y^2+xy+y=x^3-460x-3830\)
26.a2	26a1	26.a	26a	$3$	$9$	\( 2 \cdot 13 \)	\( - 2^{3} \cdot 13^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.24.0.1	3Cs.1.1	$1$	$1$		$2$	$2$	$-0.494920$	$-10218313/17576$	$[1, 0, 1, -5, -8]$	\(y^2+xy+y=x^3-5x-8\)
26.a3	26a3	26.a	26a	$3$	$9$	\( 2 \cdot 13 \)	\( - 2 \cdot 13 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.1	3B.1.1	$1$	$1$		$2$	$6$	$-1.044226$	$12167/26$	$[1, 0, 1, 0, 0]$	\(y^2+xy+y=x^3\)
26.b1	26b2	26.b	26b	$2$	$7$	\( 2 \cdot 13 \)	\( - 2 \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$1$	$1$		$0$	$14$	$0.289794$	$-1064019559329/125497034$	$[1, -1, 1, -213, -1257]$	\(y^2+xy+y=x^3-x^2-213x-1257\)
26.b2	26b1	26.b	26b	$2$	$7$	\( 2 \cdot 13 \)	\( - 2^{7} \cdot 13 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$1$	$1$		$6$	$2$	$-0.683161$	$-2146689/1664$	$[1, -1, 1, -3, 3]$	\(y^2+xy+y=x^3-x^2-3x+3\)