Elliptic curve isogeny class with LMFDB label 454860.bb (Cremona label 454860bb)

• Label: 454860.bb
• Number of curves: $4$
• Conductor: $454860$
• CM: no
• Rank: $0$

Elliptic curves in class 454860.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
454860.bb1	454860bb4	\([0, 0, 0, -6520743, 6408788958]\)	\(129348709488/6125\)	\(1451974390733664000\)	\([2]\)	\(12317184\)	\(2.5588\)	\(\Gamma_0(N)\)-optimal^*
454860.bb2	454860bb3	\([0, 0, 0, -428868, 89077833]\)	\(588791808/109375\)	\(1620507132515250000\)	\([2]\)	\(6158592\)	\(2.2123\)	\(\Gamma_0(N)\)-optimal^*
454860.bb3	454860bb2	\([0, 0, 0, -152703, -9204778]\)	\(1210991472/588245\)	\(191286173506256640\)	\([2]\)	\(4105728\)	\(2.0095\)	\(\Gamma_0(N)\)-optimal^*
454860.bb4	454860bb1	\([0, 0, 0, -125628, -17126923]\)	\(10788913152/8575\)	\(174276761576400\)	\([2]\)	\(2052864\)	\(1.6630\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 454860.bb1.

Rank

The elliptic curves in class 454860.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 454860.bb do not have complex multiplication.

Modular form 454860.2.a.bb

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.