Elliptic curve isogeny class with LMFDB label 485184.dh (Cremona label 485184dh)

• Label: 485184.dh
• Number of curves: $4$
• Conductor: $485184$
• CM: no
• Rank: $1$

Elliptic curves in class 485184.dh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485184.dh1	485184dh3	\([0, -1, 0, -419372737, 3305723454817]\)	\(661397832743623417/443352042\)	\(5467770036955120140288\)	\([2]\)	\(88473600\)	\(3.4872\)	\(\Gamma_0(N)\)-optimal^*
485184.dh2	485184dh2	\([0, -1, 0, -26373697, 50984005345]\)	\(164503536215257/4178071044\)	\(51527295472912240214016\)	\([2, 2]\)	\(44236800\)	\(3.1407\)	\(\Gamma_0(N)\)-optimal^*
485184.dh3	485184dh1	\([0, -1, 0, -3731777, -1622231583]\)	\(466025146777/177366672\)	\(2187426881674420420608\)	\([2]\)	\(22118400\)	\(2.7941\)	\(\Gamma_0(N)\)-optimal^*
485184.dh4	485184dh4	\([0, -1, 0, 4354623, 162681448545]\)	\(740480746823/927484650666\)	\(-11438478460075168693223424\)	\([2]\)	\(88473600\)	\(3.4872\)

^*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 485184.dh1.

Rank

The elliptic curves in class 485184.dh have rank \(1\).

Complex multiplication

The elliptic curves in class 485184.dh do not have complex multiplication.

Modular form 485184.2.a.dh

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.