Elliptic curve isogeny class with Cremona label 215600gv (LMFDB label 215600.dx)

• Label: 215600gv
• Number of curves: $2$
• Conductor: $215600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 215600gv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 215600gv do not have complex multiplication.

Modular form 215600.2.a.gv

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 215600gv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
215600.dx2	215600gv1	\([0, 0, 0, 104125, 3687250]\)	\(66325500/41503\)	\(-78124583152000000\)	\([2]\)	\(1327104\)	\(1.9305\)	\(\Gamma_0(N)\)-optimal
215600.dx1	215600gv2	\([0, 0, 0, -434875, 30098250]\)	\(2415899250/1294139\)	\(4872133094752000000\)	\([2]\)	\(2654208\)	\(2.2771\)