Elliptic curve isogeny class with LMFDB label 479408.q (Cremona label 479408q)

• Label: 479408.q
• Number of curves: $4$
• Conductor: $479408$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 479408.q have rank \(0\).

Complex multiplication

The elliptic curves in class 479408.q do not have complex multiplication.

Modular form 479408.2.a.q

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.

Elliptic curves in class 479408.q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479408.q1	479408q3	\([0, 0, 0, -10270811, 12668614154]\)	\(621808094281977/43266572\)	\(8337465334128361472\)	\([2]\)	\(11059200\)	\(2.6840\)	\(\Gamma_0(N)\)-optimal^*
479408.q2	479408q2	\([0, 0, 0, -682651, 171406410]\)	\(182573756217/39790864\)	\(7667696650777329664\)	\([2, 2]\)	\(5529600\)	\(2.3374\)	\(\Gamma_0(N)\)-optimal^*
479408.q3	479408q1	\([0, 0, 0, -220571, -37546166]\)	\(6158676537/403712\)	\(77795273565274112\)	\([2]\)	\(2764800\)	\(1.9908\)	\(\Gamma_0(N)\)-optimal^*
479408.q4	479408q4	\([0, 0, 0, 1512229, 1047163530]\)	\(1984699888263/3606832396\)	\(-695036345094802948096\)	\([4]\)	\(11059200\)	\(2.6840\)

^*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 479408.q1.