Elliptic curve isogeny class with LMFDB label 137904.bd (Cremona label 137904br)

• Label: 137904.bd
• Number of curves: $2$
• Conductor: $137904$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 137904.bd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(13\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 137904.bd do not have complex multiplication.

Modular form 137904.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 137904.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137904.bd1	137904br1	\([0, -1, 0, -4783432, 1444173808]\)	\(612241204436497/308834353152\)	\(6105843447002120060928\)	\([2]\)	\(7225344\)	\(2.8729\)	\(\Gamma_0(N)\)-optimal
137904.bd2	137904br2	\([0, -1, 0, 17713848, 11127003120]\)	\(31091549545392623/20700995942016\)	\(-409271310425646313242624\)	\([2]\)	\(14450688\)	\(3.2195\)