Elliptic curve isogeny class with Cremona label 414810f (LMFDB label 414810.f)

• Label: 414810f
• Number of curves: $2$
• Conductor: $414810$
• CM: no
• Rank: $1$

Elliptic curves in class 414810f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414810.f2	414810f1	\([1, -1, 0, -8701935, -9871189075]\)	\(99964020929586731506161/81651246490000000\)	\(59523758691210000000\)	\([]\)	\(19877536\)	\(2.7234\)	\(\Gamma_0(N)\)-optimal^*
414810.f1	414810f2	\([1, -1, 0, -843316485, 9426330954755]\)	\(90984613355465878035683930961/249396782289047639290\)	\(181810254288715729042410\)	\([]\)	\(139142752\)	\(3.6964\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 414810f1.

Rank

The elliptic curves in class 414810f have rank \(1\).

Complex multiplication

The elliptic curves in class 414810f do not have complex multiplication.

Modular form 414810.2.a.f

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.