Elliptic curve isogeny class with LMFDB label 227430.bn (Cremona label 227430dy)

• Label: 227430.bn
• Number of curves: $4$
• Conductor: $227430$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 227430.bn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.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 227430.bn do not have complex multiplication.

Modular form 227430.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 227430.bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227430.bn1	227430dy3	\([1, -1, 0, -5764306014, 168450243845548]\)	\(617611911727813844500009/1197723879765000\)	\(41077673861227941016485000\)	\([2]\)	\(185794560\)	\(4.1682\)
227430.bn2	227430dy4	\([1, -1, 0, -969041934, -8195840428100]\)	\(2934284984699764805929/851931751022747640\)	\(29218232358699866234299242360\)	\([2]\)	\(185794560\)	\(4.1682\)
227430.bn3	227430dy2	\([1, -1, 0, -364078134, 2573604146740]\)	\(155617476551393929129/6633105589454400\)	\(227491955945769880290945600\)	\([2, 2]\)	\(92897280\)	\(3.8216\)
227430.bn4	227430dy1	\([1, -1, 0, 11246346, 149983849588]\)	\(4586790226340951/286015269335040\)	\(-9809307597157726667304960\)	\([2]\)	\(46448640\)	\(3.4751\)	\(\Gamma_0(N)\)-optimal