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

• Label: 494190cz
• Number of curves: $4$
• Conductor: $494190$
• CM: no
• Rank: $1$

Elliptic curves in class 494190cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
494190.cz4	494190cz1	\([1, -1, 1, 9562522, 68307584757]\)	\(5495662324535111/117739817533440\)	\(-2071783714955636181565440\)	\([2]\)	\(91750400\)	\(3.3462\)	\(\Gamma_0(N)\)-optimal^*
494190.cz3	494190cz2	\([1, -1, 1, -203511398, 1058504705781]\)	\(52974743974734147769/3152005008998400\)	\(55463587288529441148518400\)	\([2, 2]\)	\(183500800\)	\(3.6927\)	\(\Gamma_0(N)\)-optimal^*
494190.cz1	494190cz3	\([1, -1, 1, -3208186598, 69942486470901]\)	\(207530301091125281552569/805586668007040\)	\(14175334858900514934119040\)	\([2]\)	\(367001600\)	\(4.0393\)	\(\Gamma_0(N)\)-optimal^*
494190.cz2	494190cz4	\([1, -1, 1, -608018918, -4455418200843]\)	\(1412712966892699019449/330160465517040000\)	\(5809598571749972109629040000\)	\([2]\)	\(367001600\)	\(4.0393\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 494190cz1.

Rank

The elliptic curves in class 494190cz have rank \(1\).

Complex multiplication

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

Modular form 494190.2.a.cz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.