Elliptic curve isogeny class with LMFDB label 455175.cc (Cremona label 455175cc)

• Label: 455175.cc
• Number of curves: $4$
• Conductor: $455175$
• CM: no
• Rank: $1$

Elliptic curves in class 455175.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
455175.cc1	455175cc3	\([1, -1, 1, -3979596380, 96629809944372]\)	\(25351269426118370449/27551475\)	\(7575057553782132421875\)	\([2]\)	\(169869312\)	\(3.9170\)	\(\Gamma_0(N)\)-optimal^*
455175.cc2	455175cc4	\([1, -1, 1, -310235630, 706575076872]\)	\(12010404962647729/6166198828125\)	\(1695347019029319268798828125\)	\([2]\)	\(169869312\)	\(3.9170\)
455175.cc3	455175cc2	\([1, -1, 1, -248787005, 1509094119372]\)	\(6193921595708449/6452105625\)	\(1773954804686734072265625\)	\([2, 2]\)	\(84934656\)	\(3.5704\)	\(\Gamma_0(N)\)-optimal^*
455175.cc4	455175cc1	\([1, -1, 1, -11770880, 35327854122]\)	\(-656008386769/1581036975\)	\(-434693463064413155859375\)	\([2]\)	\(42467328\)	\(3.2239\)	\(\Gamma_0(N)\)-optimal^*

^*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 455175.cc1.

Rank

The elliptic curves in class 455175.cc have rank \(1\).

Complex multiplication

The elliptic curves in class 455175.cc do not have complex multiplication.

Modular form 455175.2.a.cc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.