Elliptic curve isogeny class with Cremona label 190400bn (LMFDB label 190400.bw)

• Label: 190400bn
• Number of curves: $4$
• Conductor: $190400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 190400bn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 190400bn do not have complex multiplication.

Modular form 190400.2.a.bn

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 190400bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
190400.bw4	190400bn1	\([0, 0, 0, -7052300, -13441878000]\)	\(-9470133471933009/13576123187200\)	\(-55607800574771200000000\)	\([2]\)	\(12386304\)	\(3.0565\)	\(\Gamma_0(N)\)-optimal
190400.bw3	190400bn2	\([0, 0, 0, -138124300, -624499542000]\)	\(71149857462630609489/41907496960000\)	\(171653107548160000000000\)	\([2, 2]\)	\(24772608\)	\(3.4031\)
190400.bw2	190400bn3	\([0, 0, 0, -163724300, -376845142000]\)	\(118495863754334673489/53596139570691200\)	\(219529787681551155200000000\)	\([2]\)	\(49545216\)	\(3.7496\)
190400.bw1	190400bn4	\([0, 0, 0, -2209676300, -39979844438000]\)	\(291306206119284545407569/101150000000\)	\(414310400000000000000\)	\([2]\)	\(49545216\)	\(3.7496\)