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

• Label: 494190fw
• Number of curves: $2$
• Conductor: $494190$
• CM: no
• Rank: $0$

Elliptic curves in class 494190fw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
494190.fw2	494190fw1	\([1, -1, 1, 210193, -25683209]\)	\(2161700757/1848320\)	\(-878136408045296640\)	\([2]\)	\(8847360\)	\(2.1306\)	\(\Gamma_0(N)\)-optimal^*
494190.fw1	494190fw2	\([1, -1, 1, -1038287, -225939401]\)	\(260549802603/104256800\)	\(49532381766305013600\)	\([2]\)	\(17694720\)	\(2.4772\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 494190fw1.

Rank

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

Complex multiplication

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

Modular form 494190.2.a.fw

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.