Elliptic curve isogeny class with Cremona label 428400kv (LMFDB label 428400.kv)

• Label: 428400kv
• Number of curves: $8$
• Conductor: $428400$
• CM: no
• Rank: $0$

Elliptic curves in class 428400kv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
428400.kv7	428400kv1	\([0, 0, 0, -116373675, 575958348250]\)	\(-3735772816268612449/909650165760000\)	\(-42440638133698560000000000\)	\([2]\)	\(84934656\)	\(3.6359\)	\(\Gamma_0(N)\)-optimal^*
428400.kv6	428400kv2	\([0, 0, 0, -1959573675, 33386761548250]\)	\(17836145204788591940449/770635366502400\)	\(35954763659535974400000000\)	\([2, 2]\)	\(169869312\)	\(3.9825\)	\(\Gamma_0(N)\)-optimal^*
428400.kv8	428400kv3	\([0, 0, 0, 837482325, -3918237875750]\)	\(1392333139184610040991/947901937500000000\)	\(-44225312796000000000000000000\)	\([2]\)	\(254803968\)	\(4.1852\)
428400.kv3	428400kv4	\([0, 0, 0, -31352853675, 2136799271628250]\)	\(73054578035931991395831649/136386452160\)	\(6363246311976960000000\)	\([2]\)	\(339738624\)	\(4.3291\)	\(\Gamma_0(N)\)-optimal^*
428400.kv5	428400kv5	\([0, 0, 0, -2057493675, 29865656268250]\)	\(20645800966247918737249/3688936444974392640\)	\(172111018776725263011840000000\)	\([2]\)	\(339738624\)	\(4.3291\)
428400.kv4	428400kv6	\([0, 0, 0, -3662517675, -32677737875750]\)	\(116454264690812369959009/57505157319440250000\)	\(2682960619895804304000000000000\)	\([2, 2]\)	\(509607936\)	\(4.5318\)
428400.kv2	428400kv7	\([0, 0, 0, -31445517675, 2123533109124250]\)	\(73704237235978088924479009/899277423164136103500\)	\(41956687455145934044896000000000\)	\([2]\)	\(1019215872\)	\(4.8784\)
428400.kv1	428400kv8	\([0, 0, 0, -47879517675, -4029496584875750]\)	\(260174968233082037895439009/223081361502731896500\)	\(10408084002271459363104000000000\)	\([2]\)	\(1019215872\)	\(4.8784\)

^*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 428400kv1.

Rank

The elliptic curves in class 428400kv have rank \(0\).

Complex multiplication

The elliptic curves in class 428400kv do not have complex multiplication.

Modular form 428400.2.a.kv

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.