Elliptic curve isogeny class with Cremona label 101400l (LMFDB label 101400.c)

• Label: 101400l
• Number of curves: $4$
• Conductor: $101400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 101400l have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 101400l do not have complex multiplication.

Modular form 101400.2.a.l

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.

Elliptic curves in class 101400l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
101400.c3	101400l1	\([0, -1, 0, -470383, 124033012]\)	\(9538484224/26325\)	\(31766436731250000\)	\([2]\)	\(1548288\)	\(2.0394\)	\(\Gamma_0(N)\)-optimal
101400.c2	101400l2	\([0, -1, 0, -660508, 14521012]\)	\(1650587344/950625\)	\(18353941222500000000\)	\([2, 2]\)	\(3096576\)	\(2.3859\)
101400.c4	101400l3	\([0, -1, 0, 2634992, 113386012]\)	\(26198797244/15234375\)	\(-1176534693750000000000\)	\([2]\)	\(6193152\)	\(2.7325\)
101400.c1	101400l4	\([0, -1, 0, -6998008, -7096153988]\)	\(490757540836/2142075\)	\(165430190218800000000\)	\([2]\)	\(6193152\)	\(2.7325\)