Elliptic curve isogeny class with Cremona label 485520ig (LMFDB label 485520.ig)

• Label: 485520ig
• Number of curves: $8$
• Conductor: $485520$
• CM: no
• Rank: $1$

Elliptic curves in class 485520ig

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485520.ig7	485520ig1	\([0, 1, 0, -149475520, -838474525900]\)	\(-3735772816268612449/909650165760000\)	\(-89934821957195519754240000\)	\([2]\)	\(127401984\)	\(3.6985\)	\(\Gamma_0(N)\)-optimal^*
485520.ig6	485520ig2	\([0, 1, 0, -2516963520, -48602071428300]\)	\(17836145204788591940449/770635366502400\)	\(76190778707115903654297600\)	\([2, 2]\)	\(254803968\)	\(4.0451\)	\(\Gamma_0(N)\)-optimal^*
485520.ig8	485520ig3	\([0, 1, 0, 1075699520, 5704151954228]\)	\(1392333139184610040991/947901937500000000\)	\(-93716678335037184000000000000\)	\([2]\)	\(382205952\)	\(4.2478\)	\(\Gamma_0(N)\)-optimal^*
485520.ig5	485520ig4	\([0, 1, 0, -2642736320, -43476427355340]\)	\(20645800966247918737249/3688936444974392640\)	\(364715859874546096460153487360\)	\([4]\)	\(509607936\)	\(4.3917\)	\(\Gamma_0(N)\)-optimal^*
485520.ig3	485520ig5	\([0, 1, 0, -40270998720, -3110560037446860]\)	\(73054578035931991395831649/136386452160\)	\(13484185189077807267840\)	\([2]\)	\(509607936\)	\(4.3917\)
485520.ig4	485520ig6	\([0, 1, 0, -4704300480, 47567535954228]\)	\(116454264690812369959009/57505157319440250000\)	\(5685390142070145334281216000000\)	\([2, 2]\)	\(764411904\)	\(4.5944\)	\(\Gamma_0(N)\)-optimal^*
485520.ig1	485520ig7	\([0, 1, 0, -61498580480, 5865732603138228]\)	\(260174968233082037895439009/223081361502731896500\)	\(22055492632109608305744316416000\)	\([4]\)	\(1528823808\)	\(4.9410\)	\(\Gamma_0(N)\)-optimal^*
485520.ig2	485520ig8	\([0, 1, 0, -40390020480, -3091248475229772]\)	\(73704237235978088924479009/899277423164136103500\)	\(88909295008835721312757315584000\)	\([2]\)	\(1528823808\)	\(4.9410\)

^*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 485520ig1.

Rank

The elliptic curves in class 485520ig have rank \(1\).

Complex multiplication

The elliptic curves in class 485520ig do not have complex multiplication.

Modular form 485520.2.a.ig

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.