Elliptic curve isogeny class with LMFDB label 481650.is (Cremona label 481650is)

• Label: 481650.is
• Number of curves: $4$
• Conductor: $481650$
• CM: no
• Rank: $1$

Elliptic curves in class 481650.is

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481650.is1	481650is3	\([1, 0, 0, -2080728088, 36531629713292]\)	\(13209596798923694545921/92340\)	\(6964180360312500\)	\([2]\)	\(176947200\)	\(3.5747\)	\(\Gamma_0(N)\)-optimal^*
481650.is2	481650is4	\([1, 0, 0, -131651088, 555980666292]\)	\(3345930611358906241/165622259047500\)	\(12491047040168819179687500\)	\([2]\)	\(176947200\)	\(3.5747\)
481650.is3	481650is2	\([1, 0, 0, -130045588, 570797825792]\)	\(3225005357698077121/8526675600\)	\(643072414471256250000\)	\([2, 2]\)	\(88473600\)	\(3.2281\)	\(\Gamma_0(N)\)-optimal^*
481650.is4	481650is1	\([1, 0, 0, -8027588, 9148971792]\)	\(-758575480593601/40535043840\)	\(-3057108037848540000000\)	\([2]\)	\(44236800\)	\(2.8815\)	\(\Gamma_0(N)\)-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 481650.is1.

Rank

The elliptic curves in class 481650.is have rank \(1\).

Complex multiplication

The elliptic curves in class 481650.is do not have complex multiplication.

Modular form 481650.2.a.is

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.