Elliptic curve isogeny class with LMFDB label 370.b (Cremona label 370a)

• Label: 370.b
• Number of curves: $4$
• Conductor: $370$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 370.b have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 + T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 370.b do not have complex multiplication.

Modular form 370.2.a.b

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 370.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
370.b1	370a3	\([1, -1, 0, -395, -2925]\)	\(6825481747209/46250\)	\(46250\)	\([2]\)	\(64\)	\(0.076511\)
370.b2	370a2	\([1, -1, 0, -25, -39]\)	\(1767172329/136900\)	\(136900\)	\([2, 2]\)	\(32\)	\(-0.27006\)
370.b3	370a1	\([1, -1, 0, -5, 5]\)	\(15438249/2960\)	\(2960\)	\([2]\)	\(16\)	\(-0.61664\)	\(\Gamma_0(N)\)-optimal
370.b4	370a4	\([1, -1, 0, 25, -209]\)	\(1689410871/18741610\)	\(-18741610\)	\([2]\)	\(64\)	\(0.076511\)