Elliptic curve isogeny class with LMFDB label 387600.bd (Cremona label 387600bd)

• Label: 387600.bd
• Number of curves: $2$
• Conductor: $387600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 387600.bd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(17\)	\(1 - T\)
\(19\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 387600.bd do not have complex multiplication.

Modular form 387600.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 387600.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
387600.bd1	387600bd2	\([0, -1, 0, -21608, 407712]\)	\(69737687428/36026451\)	\(576423216000000\)	\([2]\)	\(1310720\)	\(1.5244\)
387600.bd2	387600bd1	\([0, -1, 0, -12108, -504288]\)	\(49081386832/497097\)	\(1988388000000\)	\([2]\)	\(655360\)	\(1.1778\)	\(\Gamma_0(N)\)-optimal