Elliptic curve isogeny class with Cremona label 187850b (LMFDB label 187850.bd)

• Label: 187850b
• Number of curves: $4$
• Conductor: $187850$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 187850b have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 187850b do not have complex multiplication.

Modular form 187850.2.a.b

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 187850b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
187850.bd2	187850b1	\([1, 0, 0, -234963, 43558417]\)	\(3803721481/26000\)	\(9805887406250000\)	\([2]\)	\(2654208\)	\(1.9025\)	\(\Gamma_0(N)\)-optimal
187850.bd3	187850b2	\([1, 0, 0, -90463, 96589917]\)	\(-217081801/10562500\)	\(-3983641758789062500\)	\([2]\)	\(5308416\)	\(2.2490\)
187850.bd1	187850b3	\([1, 0, 0, -1499338, -678399708]\)	\(988345570681/44994560\)	\(16969676509760000000\)	\([2]\)	\(7962624\)	\(2.4518\)
187850.bd4	187850b4	\([1, 0, 0, 812662, -2581175708]\)	\(157376536199/7722894400\)	\(-2912685882183025000000\)	\([2]\)	\(15925248\)	\(2.7983\)