Elliptic curve isogeny class with Cremona label 46410i (LMFDB label 46410.h)

• Label: 46410i
• Number of curves: $4$
• Conductor: $46410$
• CM: no
• Rank: $1$

Elliptic curves in class 46410i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46410.h3	46410i1	\([1, 1, 0, -8507197498, 302011019305108]\)	\(68089988046149164570007733493682089/28060999477855518720000\)	\(28060999477855518720000\)	\([2]\)	\(46448640\)	\(4.0896\)	\(\Gamma_0(N)\)-optimal
46410.h2	46410i2	\([1, 1, 0, -8508508218, 301913300148372]\)	\(68121465154900977371934154073952169/43710573588218598297600000000\)	\(43710573588218598297600000000\)	\([2, 2]\)	\(92897280\)	\(4.4362\)
46410.h4	46410i3	\([1, 1, 0, -6883079738, 420764955691668]\)	\(-36063852191950372967514090386599849/55613397696702747890625000000000\)	\(-55613397696702747890625000000000\)	\([2]\)	\(185794560\)	\(4.7828\)
46410.h1	46410i4	\([1, 1, 0, -10154908218, 176807644788372]\)	\(115811508824614211679593714547552169/53515175226614393876135522880000\)	\(53515175226614393876135522880000\)	\([2]\)	\(185794560\)	\(4.7828\)

Rank

The elliptic curves in class 46410i have rank \(1\).

Complex multiplication

The elliptic curves in class 46410i do not have complex multiplication.

Modular form 46410.2.a.i

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.