Elliptic curve isogeny class with Cremona label 395850g (LMFDB label 395850.g)

• Label: 395850g
• Number of curves: $2$
• Conductor: $395850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 395850g have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 395850g do not have complex multiplication.

Modular form 395850.2.a.g

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 395850g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
395850.g2	395850g1	\([1, 1, 0, 2310200, -185336000]\)	\(87267418871946300287/51461562131546112\)	\(-804086908305408000000\)	\([2]\)	\(22118400\)	\(2.7007\)	\(\Gamma_0(N)\)-optimal
395850.g1	395850g2	\([1, 1, 0, -9337800, -1501560000]\)	\(5762851946879949436033/3272968937100635136\)	\(51140139642197424000000\)	\([2]\)	\(44236800\)	\(3.0473\)