Elliptic curve isogeny class with LMFDB label 408135.bl (Cremona label 408135bl)

• Label: 408135.bl
• Number of curves: $4$
• Conductor: $408135$
• CM: no
• Rank: $1$

Elliptic curves in class 408135.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
408135.bl1	408135bl3	\([1, 1, 0, -853622, 303201111]\)	\(14251520160844849/264449745\)	\(1276448409213705\)	\([2]\)	\(3686400\)	\(2.0235\)	\(\Gamma_0(N)\)-optimal^*
408135.bl2	408135bl2	\([1, 1, 0, -55097, 4393056]\)	\(3832302404449/472410225\)	\(2280233925722025\)	\([2, 2]\)	\(1843200\)	\(1.6769\)	\(\Gamma_0(N)\)-optimal^*
408135.bl3	408135bl1	\([1, 1, 0, -13692, -550701]\)	\(58818484369/7455105\)	\(35984367909945\)	\([2]\)	\(921600\)	\(1.3304\)	\(\Gamma_0(N)\)-optimal^*
408135.bl4	408135bl4	\([1, 1, 0, 80948, 22813549]\)	\(12152722588271/53476250625\)	\(-258119647803005625\)	\([2]\)	\(3686400\)	\(2.0235\)

^*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 408135.bl1.

Rank

The elliptic curves in class 408135.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 408135.bl do not have complex multiplication.

Modular form 408135.2.a.bl

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.