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

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

Elliptic curves in class 479370.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479370.z1	479370z4	\([1, 0, 1, -522279, -145110848]\)	\(26487576322129/44531250\)	\(26488226013281250\)	\([2]\)	\(6193152\)	\(2.0466\)
479370.z2	479370z2	\([1, 0, 1, -42909, -724604]\)	\(14688124849/8122500\)	\(4831452424822500\)	\([2, 2]\)	\(3096576\)	\(1.7000\)
479370.z3	479370z1	\([1, 0, 1, -26089, 1610012]\)	\(3301293169/22800\)	\(13561971718800\)	\([2]\)	\(1548288\)	\(1.3534\)	\(\Gamma_0(N)\)-optimal^*
479370.z4	479370z3	\([1, 0, 1, 167341, -5686504]\)	\(871257511151/527800050\)	\(-313947778564966050\)	\([2]\)	\(6193152\)	\(2.0466\)

^*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 479370.z1.

Rank

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

Complex multiplication

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

Modular form 479370.2.a.z

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.