Elliptic curve isogeny class with LMFDB label 377520.bd (Cremona label 377520bd)

• Label: 377520.bd
• Number of curves: $4$
• Conductor: $377520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 377520.bd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 377520.bd do not have complex multiplication.

Modular form 377520.2.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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 377520.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
377520.bd1	377520bd4	\([0, -1, 0, -2315496, -1286386704]\)	\(189208196468929/10860320250\)	\(78805892310672384000\)	\([2]\)	\(9953280\)	\(2.5719\)
377520.bd2	377520bd2	\([0, -1, 0, -398856, 96660720]\)	\(967068262369/4928040\)	\(35759404934922240\)	\([2]\)	\(3317760\)	\(2.0226\)
377520.bd3	377520bd1	\([0, -1, 0, -11656, 3113200]\)	\(-24137569/561600\)	\(-4075145861529600\)	\([2]\)	\(1658880\)	\(1.6760\)	\(\Gamma_0(N)\)-optimal
377520.bd4	377520bd3	\([0, -1, 0, 104504, -82194704]\)	\(17394111071/411937500\)	\(-2989147789056000000\)	\([2]\)	\(4976640\)	\(2.2253\)