Elliptic curve isogeny class with LMFDB label 424830.gz (Cremona label 424830gz)

• Label: 424830.gz
• Number of curves: $8$
• Conductor: $424830$
• CM: no
• Rank: $0$

Elliptic curves in class 424830.gz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
424830.gz1	424830gz7	\([1, 0, 0, -188339402721, 31436754839645301]\)	\(260174968233082037895439009/223081361502731896500\)	\(633497717938247877822879170416500\)	\([2]\)	\(3057647616\)	\(5.2208\)	\(\Gamma_0(N)\)-optimal^*
424830.gz2	424830gz8	\([1, 0, 0, -123694437721, -16567097949715699]\)	\(73704237235978088924479009/899277423164136103500\)	\(2553732824339480902520650737583500\)	\([2]\)	\(3057647616\)	\(5.2208\)
424830.gz3	424830gz5	\([1, 0, 0, -123329933581, -16670596035724975]\)	\(73054578035931991395831649/136386452160\)	\(387304908034622789856960\)	\([2]\)	\(1019215872\)	\(4.6715\)
424830.gz4	424830gz6	\([1, 0, 0, -14406920221, 254939466464801]\)	\(116454264690812369959009/57505157319440250000\)	\(163300894732522101668176460250000\)	\([2, 2]\)	\(1528823808\)	\(4.8742\)	\(\Gamma_0(N)\)-optimal^*
424830.gz5	424830gz4	\([1, 0, 0, -8093379981, -233002431167535]\)	\(20645800966247918737249/3688936444974392640\)	\(10475697314057732837509911531840\)	\([2]\)	\(1019215872\)	\(4.6715\)	\(\Gamma_0(N)\)-optimal^*
424830.gz6	424830gz2	\([1, 0, 0, -7708200781, -260472872460655]\)	\(17836145204788591940449/770635366502400\)	\(2188420147488642321539174400\)	\([2, 2]\)	\(509607936\)	\(4.3249\)	\(\Gamma_0(N)\)-optimal^*
424830.gz7	424830gz1	\([1, 0, 0, -457768781, -4493470527855]\)	\(-3735772816268612449/909650165760000\)	\(-2583188932725121021378560000\)	\([2]\)	\(254803968\)	\(3.9783\)	\(\Gamma_0(N)\)-optimal^*
424830.gz8	424830gz3	\([1, 0, 0, 3294329779, 30569042214801]\)	\(1392333139184610040991/947901937500000000\)	\(-2691814816757517006937500000000\)	\([2]\)	\(764411904\)	\(4.5276\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 6 curves highlighted, and conditionally curve 424830.gz1.

Rank

The elliptic curves in class 424830.gz have rank \(0\).

Complex multiplication

The elliptic curves in class 424830.gz do not have complex multiplication.

Modular form 424830.2.a.gz

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.