Elliptic curve isogeny class with Cremona label 110400ei (LMFDB label 110400.jl)

• Label: 110400ei
• Number of curves: $4$
• Conductor: $110400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 110400ei have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110400ei do not have complex multiplication.

Modular form 110400.2.a.ei

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 110400ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110400.jl3	110400ei1	\([0, 1, 0, -16533, -562437]\)	\(31238127616/9703125\)	\(155250000000000\)	\([2]\)	\(387072\)	\(1.4274\)	\(\Gamma_0(N)\)-optimal
110400.jl4	110400ei2	\([0, 1, 0, 45967, -3749937]\)	\(41957807024/48205125\)	\(-12340512000000000\)	\([2]\)	\(774144\)	\(1.7740\)
110400.jl1	110400ei3	\([0, 1, 0, -1216533, -516862437]\)	\(12444451776495616/912525\)	\(14600400000000\)	\([2]\)	\(1161216\)	\(1.9767\)
110400.jl2	110400ei4	\([0, 1, 0, -1214033, -519089937]\)	\(-772993034343376/6661615005\)	\(-1705373441280000000\)	\([2]\)	\(2322432\)	\(2.3233\)