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

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

Elliptic curves in class 463680.ko

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
463680.ko1	463680ko6	\([0, 0, 0, -51197772, -141001805936]\)	\(155324313723954725282/13018359375\)	\(1243923609600000000\)	\([2]\)	\(29360128\)	\(2.9145\)
463680.ko2	463680ko3	\([0, 0, 0, -4406412, 3556441744]\)	\(198048499826486404/242568272835\)	\(11588879705487114240\)	\([2]\)	\(14680064\)	\(2.5680\)	\(\Gamma_0(N)\)-optimal^*
463680.ko3	463680ko4	\([0, 0, 0, -3206892, -2192984624]\)	\(76343005935514084/694180580625\)	\(33164993709711360000\)	\([2, 2]\)	\(14680064\)	\(2.5680\)
463680.ko4	463680ko5	\([0, 0, 0, -938892, -5234826224]\)	\(-957928673903042/123339801817575\)	\(-11785301593294395801600\)	\([2]\)	\(29360128\)	\(2.9145\)
463680.ko5	463680ko2	\([0, 0, 0, -349212, 23431984]\)	\(394315384276816/208332909225\)	\(2488314934477209600\)	\([2, 2]\)	\(7340032\)	\(2.2214\)	\(\Gamma_0(N)\)-optimal^*
463680.ko6	463680ko1	\([0, 0, 0, 82968, 2860216]\)	\(84611246065664/53699121315\)	\(-40086179265162240\)	\([2]\)	\(3670016\)	\(1.8748\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 463680.ko1.

Rank

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

Complex multiplication

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

Modular form 463680.2.a.ko

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.