Elliptic curve isogeny class with LMFDB label 448448.cd (Cremona label 448448cd)

• Label: 448448.cd
• Number of curves: $4$
• Conductor: $448448$
• CM: no
• Rank: $0$

Elliptic curves in class 448448.cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
448448.cd1	448448cd4	\([0, 0, 0, -31095596, -66741571120]\)	\(107818231938348177/4463459\)	\(137657447321698304\)	\([2]\)	\(14942208\)	\(2.7749\)
448448.cd2	448448cd3	\([0, 0, 0, -3153836, 404064976]\)	\(112489728522417/62811265517\)	\(1937160949415158218752\)	\([2]\)	\(14942208\)	\(2.7749\)	\(\Gamma_0(N)\)-optimal^*
448448.cd3	448448cd2	\([0, 0, 0, -1946476, -1039454640]\)	\(26444947540257/169338169\)	\(5222554991245656064\)	\([2, 2]\)	\(7471104\)	\(2.4283\)	\(\Gamma_0(N)\)-optimal^*
448448.cd4	448448cd1	\([0, 0, 0, -49196, -35414064]\)	\(-426957777/17320303\)	\(-534175108994695168\)	\([2]\)	\(3735552\)	\(2.0818\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 448448.cd1.

Rank

The elliptic curves in class 448448.cd have rank \(0\).

Complex multiplication

The elliptic curves in class 448448.cd do not have complex multiplication.

Modular form 448448.2.a.cd

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.