Elliptic curve isogeny class with Cremona label 3520bd (LMFDB label 3520.ba)

• Label: 3520bd
• Number of curves: $2$
• Conductor: $3520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3520bd have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3520bd do not have complex multiplication.

Modular form 3520.2.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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 3520bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3520.ba1	3520bd1	\([0, 1, 0, -65, -577]\)	\(-117649/440\)	\(-115343360\)	\([]\)	\(768\)	\(0.23262\)	\(\Gamma_0(N)\)-optimal
3520.ba2	3520bd2	\([0, 1, 0, 575, 13375]\)	\(80062991/332750\)	\(-87228416000\)	\([]\)	\(2304\)	\(0.78192\)