Elliptic curve isogeny class with Cremona label 479370bm (LMFDB label 479370.bm)

• Label: 479370bm
• Number of curves: $4$
• Conductor: $479370$
• CM: no
• Rank: $1$

Elliptic curves in class 479370bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479370.bm4	479370bm1	\([1, 0, 1, -1597918, 812431568]\)	\(-758575480593601/40535043840\)	\(-24111189393789392640\)	\([2]\)	\(24084480\)	\(2.4780\)	\(\Gamma_0(N)\)-optimal^*
479370.bm3	479370bm2	\([1, 0, 1, -25885998, 50690432656]\)	\(3225005357698077121/8526675600\)	\(5071865497481667600\)	\([2, 2]\)	\(48168960\)	\(2.8246\)	\(\Gamma_0(N)\)-optimal^*
479370.bm1	479370bm3	\([1, 0, 1, -414175698, 3244295557216]\)	\(13209596798923694545921/92340\)	\(54925985461140\)	\([2]\)	\(96337920\)	\(3.1711\)	\(\Gamma_0(N)\)-optimal^*
479370.bm2	479370bm4	\([1, 0, 1, -26205578, 49374530048]\)	\(3345930611358906241/165622259047500\)	\(98515982158156246747500\)	\([2]\)	\(96337920\)	\(3.1711\)

^*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 479370bm1.

Rank

The elliptic curves in class 479370bm have rank \(1\).

Complex multiplication

The elliptic curves in class 479370bm do not have complex multiplication.

Modular form 479370.2.a.bm

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.