Elliptic curve isogeny class with LMFDB label 482790.fw (Cremona label 482790fw)

• Label: 482790.fw
• Number of curves: $4$
• Conductor: $482790$
• CM: no
• Rank: $2$

Elliptic curves in class 482790.fw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
482790.fw1	482790fw3	\([1, 1, 1, -1517824910, 22759806218315]\)	\(218289391029690300712901881/306514992000\)	\(543010005742512000\)	\([2]\)	\(137625600\)	\(3.5679\)	\(\Gamma_0(N)\)-optimal^*
482790.fw2	482790fw4	\([1, 1, 1, -99278990, 320672003147]\)	\(61085713691774408830201/10268551781250000000\)	\(18191365862143031250000000\)	\([2]\)	\(137625600\)	\(3.5679\)
482790.fw3	482790fw2	\([1, 1, 1, -94864910, 355585610315]\)	\(53294746224000958661881/1997017344000000\)	\(3537838042953984000000\)	\([2, 2]\)	\(68812800\)	\(3.2213\)	\(\Gamma_0(N)\)-optimal^*
482790.fw4	482790fw1	\([1, 1, 1, -5654030, 6093066827]\)	\(-11283450590382195961/2530373271552000\)	\(-4482710603323932672000\)	\([2]\)	\(34406400\)	\(2.8747\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 482790.fw1.

Rank

The elliptic curves in class 482790.fw have rank \(2\).

Complex multiplication

The elliptic curves in class 482790.fw do not have complex multiplication.

Modular form 482790.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.