Elliptic curve isogeny class with Cremona label 110400bd (LMFDB label 110400.dx)

• Label: 110400bd
• Number of curves: $2$
• Conductor: $110400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 110400bd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110400bd do not have complex multiplication.

Modular form 110400.2.a.bd

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 110400bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110400.dx2	110400bd1	\([0, -1, 0, -2433, 100737]\)	\(-389017/828\)	\(-3391488000000\)	\([2]\)	\(196608\)	\(1.0933\)	\(\Gamma_0(N)\)-optimal
110400.dx1	110400bd2	\([0, -1, 0, -50433, 4372737]\)	\(3463512697/3174\)	\(13000704000000\)	\([2]\)	\(393216\)	\(1.4399\)