Elliptic curve isogeny class with Cremona label 147600bd (LMFDB label 147600.m)

• Label: 147600bd
• Number of curves: $2$
• Conductor: $147600$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 147600bd have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(41\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 147600bd do not have complex multiplication.

Modular form 147600.2.a.bd

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 147600bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
147600.m2	147600bd1	\([0, 0, 0, -5475, 81250]\)	\(389017/164\)	\(7651584000000\)	\([2]\)	\(294912\)	\(1.1690\)	\(\Gamma_0(N)\)-optimal
147600.m1	147600bd2	\([0, 0, 0, -41475, -3194750]\)	\(169112377/3362\)	\(156857472000000\)	\([2]\)	\(589824\)	\(1.5156\)