Elliptic curve isogeny class with Cremona label 444675ft (LMFDB label 444675.ft)

• Label: 444675ft
• Number of curves: $4$
• Conductor: $444675$
• CM: no
• Rank: $1$

Elliptic curves in class 444675ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
444675.ft3	444675ft1	\([1, 1, 0, -30166875, 63715329000]\)	\(932288503609/779625\)	\(2538926532451353515625\)	\([2]\)	\(39813120\)	\(3.0351\)	\(\Gamma_0(N)\)-optimal
444675.ft2	444675ft2	\([1, 1, 0, -36837000, 33452971875]\)	\(1697509118089/833765625\)	\(2715240874982697509765625\)	\([2, 2]\)	\(79626240\)	\(3.3816\)
444675.ft4	444675ft3	\([1, 1, 0, 134362875, 256526409000]\)	\(82375335041831/56396484375\)	\(-183660773470149993896484375\)	\([2]\)	\(159252480\)	\(3.7282\)
444675.ft1	444675ft4	\([1, 1, 0, -314758875, -2126277918750]\)	\(1058993490188089/13182390375\)	\(42929768394059769427734375\)	\([2]\)	\(159252480\)	\(3.7282\)

Rank

The elliptic curves in class 444675ft have rank \(1\).

Complex multiplication

The elliptic curves in class 444675ft do not have complex multiplication.

Modular form 444675.2.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 Cremona 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 Cremona labels.