Elliptic curve isogeny class with Cremona label 481338df (LMFDB label 481338.df)

• Label: 481338df
• Number of curves: $4$
• Conductor: $481338$
• CM: no
• Rank: $0$

Elliptic curves in class 481338df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481338.df4	481338df1	\([1, -1, 1, 975020881, -1286710394570697]\)	\(79374649975090937760383/553856914190911653543936\)	\(-715288464086743951460818678185984\)	\([2]\)	\(2269347840\)	\(4.9831\)	\(\Gamma_0(N)\)-optimal^*
481338.df3	481338df2	\([1, -1, 1, -171737242799, -26863669522941897]\)	\(433744050935826360922067531137/9612122270219882316693504\)	\(12413748026100540598959174406373376\)	\([2, 2]\)	\(4538695680\)	\(5.3297\)	\(\Gamma_0(N)\)-optimal^*
481338.df2	481338df3	\([1, -1, 1, -373858430639, 48387423133967415]\)	\(4474676144192042711273397261697/1806328356954994499451382272\)	\(2332815214503773770612648277062445568\)	\([2]\)	\(9077391360\)	\(5.6763\)	\(\Gamma_0(N)\)-optimal^*
481338.df1	481338df4	\([1, -1, 1, -2733012273839, -1739042218942772169]\)	\(1748094148784980747354970849498497/887694600425282263291392\)	\(1146429142703505820824657281422848\)	\([2]\)	\(9077391360\)	\(5.6763\)

^*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 481338df1.

Rank

The elliptic curves in class 481338df have rank \(0\).

Complex multiplication

The elliptic curves in class 481338df do not have complex multiplication.

Modular form 481338.2.a.df

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.