Elliptic curve isogeny class with Cremona label 101640t (LMFDB label 101640.bn)

• Label: 101640t
• Number of curves: $4$
• Conductor: $101640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 101640t have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 101640t do not have complex multiplication.

Modular form 101640.2.a.t

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 101640t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
101640.bn3	101640t1	\([0, 1, 0, -4396, 110240]\)	\(20720464/105\)	\(47619559680\)	\([2]\)	\(92160\)	\(0.89543\)	\(\Gamma_0(N)\)-optimal
101640.bn2	101640t2	\([0, 1, 0, -6816, -27216]\)	\(19307236/11025\)	\(20000215065600\)	\([2, 2]\)	\(184320\)	\(1.2420\)
101640.bn4	101640t3	\([0, 1, 0, 27064, -189840]\)	\(604223422/354375\)	\(-1285728111360000\)	\([2]\)	\(368640\)	\(1.5886\)
101640.bn1	101640t4	\([0, 1, 0, -79416, -8623056]\)	\(15267472418/36015\)	\(130668071761920\)	\([2]\)	\(368640\)	\(1.5886\)