Elliptic curve isogeny class with Cremona label 460845bc (LMFDB label 460845.bc)

• Label: 460845bc
• Number of curves: $4$
• Conductor: $460845$
• CM: no
• Rank: $1$

Elliptic curves in class 460845bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
460845.bc3	460845bc1	\([1, -1, 1, -433242452, -3470811824546]\)	\(104857852278310619039721/47155625\)	\(4044355039580625\)	\([2]\)	\(54263808\)	\(3.2381\)	\(\Gamma_0(N)\)-optimal^*
460845.bc2	460845bc2	\([1, -1, 1, -433244657, -3470774726744]\)	\(104859453317683374662841/2223652969140625\)	\(190714089613324109765625\)	\([2, 2]\)	\(108527616\)	\(3.5847\)	\(\Gamma_0(N)\)-optimal^*
460845.bc1	460845bc3	\([1, -1, 1, -448404032, -3214835966744]\)	\(116256292809537371612841/15216540068579856875\)	\(1305063616723168302903931875\)	\([2]\)	\(217055232\)	\(3.9312\)	\(\Gamma_0(N)\)-optimal^*
460845.bc4	460845bc4	\([1, -1, 1, -418120562, -3724339253876]\)	\(-94256762600623910012361/15323275604248046875\)	\(-1314217909590286102294921875\)	\([2]\)	\(217055232\)	\(3.9312\)

^*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 460845bc1.

Rank

The elliptic curves in class 460845bc have rank \(1\).

Complex multiplication

The elliptic curves in class 460845bc do not have complex multiplication.

Modular form 460845.2.a.bc

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.