Elliptic curve isogeny class with LMFDB label 494190.bo (Cremona label 494190bo)

• Label: 494190.bo
• Number of curves: $4$
• Conductor: $494190$
• CM: no
• Rank: $0$

Elliptic curves in class 494190.bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
494190.bo1	494190bo4	\([1, -1, 0, -1280940534, -17645488463952]\)	\(13209596798923694545921/92340\)	\(1624841215544340\)	\([2]\)	\(157286400\)	\(3.4534\)
494190.bo2	494190bo3	\([1, -1, 0, -81047214, -268538123880]\)	\(3345930611358906241/165622259047500\)	\(2914336936451586129547500\)	\([2]\)	\(157286400\)	\(3.4534\)	\(\Gamma_0(N)\)-optimal^*
494190.bo3	494190bo2	\([1, -1, 0, -80058834, -275695378812]\)	\(3225005357698077121/8526675600\)	\(150037837843364355600\)	\([2, 2]\)	\(78643200\)	\(3.1068\)	\(\Gamma_0(N)\)-optimal^*
494190.bo4	494190bo1	\([1, -1, 0, -4941954, -4418278380]\)	\(-758575480593601/40535043840\)	\(-713266297434792195840\)	\([2]\)	\(39321600\)	\(2.7603\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 494190.bo1.

Rank

The elliptic curves in class 494190.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 494190.bo do not have complex multiplication.

Modular form 494190.2.a.bo

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.