Elliptic curve isogeny class with Cremona label 104742d (LMFDB label 104742.bd)

• Label: 104742d
• Number of curves: $2$
• Conductor: $104742$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 104742d have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 104742d do not have complex multiplication.

Modular form 104742.2.a.d

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 104742d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
104742.bd2	104742d1	\([1, -1, 0, -1750560, -890694352]\)	\(203608800387/93104\)	\(271285541698322448\)	\([2]\)	\(3244032\)	\(2.3023\)	\(\Gamma_0(N)\)-optimal
104742.bd1	104742d2	\([1, -1, 0, -2036220, -580181932]\)	\(320434759107/135443044\)	\(394652641785634581228\)	\([2]\)	\(6488064\)	\(2.6488\)