Elliptic curve isogeny class with LMFDB label 463680.kp (Cremona label 463680kp)

• Label: 463680.kp
• Number of curves: $6$
• Conductor: $463680$
• CM: no
• Rank: $0$

Elliptic curves in class 463680.kp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
463680.kp1	463680kp5	\([0, 0, 0, -48781452, 131138341616]\)	\(67176973097223766561/91487391870\)	\(17483512852835205120\)	\([2]\)	\(25165824\)	\(2.9665\)	\(\Gamma_0(N)\)-optimal^*
463680.kp2	463680kp3	\([0, 0, 0, -3075852, 2010880496]\)	\(16840406336564161/604708416900\)	\(115561578081838694400\)	\([2, 2]\)	\(12582912\)	\(2.6199\)	\(\Gamma_0(N)\)-optimal^*
463680.kp3	463680kp2	\([0, 0, 0, -483852, -86565904]\)	\(65553197996161/20996010000\)	\(4012399995125760000\)	\([2, 2]\)	\(6291456\)	\(2.2733\)	\(\Gamma_0(N)\)-optimal^*
463680.kp4	463680kp1	\([0, 0, 0, -437772, -111467536]\)	\(48551226272641/9273600\)	\(1772212558233600\)	\([2]\)	\(3145728\)	\(1.9267\)	\(\Gamma_0(N)\)-optimal^*
463680.kp5	463680kp6	\([0, 0, 0, 1157748, 7119988976]\)	\(898045580910239/115117148363070\)	\(-21999229640816205496320\)	\([2]\)	\(25165824\)	\(2.9665\)
463680.kp6	463680kp4	\([0, 0, 0, 1370868, -590307856]\)	\(1490881681033919/1650501562500\)	\(-315415760486400000000\)	\([2]\)	\(12582912\)	\(2.6199\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 463680.kp1.

Rank

The elliptic curves in class 463680.kp have rank \(0\).

Complex multiplication

The elliptic curves in class 463680.kp do not have complex multiplication.

Modular form 463680.2.a.kp

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.