Elliptic curve isogeny class with LMFDB label 446160.ft (Cremona label 446160ft)

• Label: 446160.ft
• Number of curves: $6$
• Conductor: $446160$
• CM: no
• Rank: $2$

Elliptic curves in class 446160.ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446160.ft1	446160ft5	\([0, 1, 0, -462613896, 3829645986804]\)	\(553808571467029327441/12529687500\)	\(247719560774400000000\)	\([2]\)	\(70778880\)	\(3.4374\)	\(\Gamma_0(N)\)-optimal^*
446160.ft2	446160ft4	\([0, 1, 0, -31974856, -69450519436]\)	\(182864522286982801/463015182960\)	\(9154092450807704125440\)	\([2]\)	\(35389440\)	\(3.0908\)
446160.ft3	446160ft3	\([0, 1, 0, -28946376, 59687501940]\)	\(135670761487282321/643043610000\)	\(12713364210239447040000\)	\([2, 2]\)	\(35389440\)	\(3.0908\)	\(\Gamma_0(N)\)-optimal^*
446160.ft4	446160ft6	\([0, 1, 0, -14074376, 120954193140]\)	\(-15595206456730321/310672490129100\)	\(-6142184535685329067622400\)	\([2]\)	\(70778880\)	\(3.4374\)
446160.ft5	446160ft2	\([0, 1, 0, -2771656, -168847756]\)	\(119102750067601/68309049600\)	\(1350511556160415334400\)	\([2, 2]\)	\(17694720\)	\(2.7442\)	\(\Gamma_0(N)\)-optimal^*
446160.ft6	446160ft1	\([0, 1, 0, 689464, -20711820]\)	\(1833318007919/1070530560\)	\(-21165041835143331840\)	\([2]\)	\(8847360\)	\(2.3977\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 446160.ft1.

Rank

The elliptic curves in class 446160.ft have rank \(2\).

Complex multiplication

The elliptic curves in class 446160.ft do not have complex multiplication.

Modular form 446160.2.a.ft

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.