Elliptic curve isogeny class with LMFDB label 6300.y (Cremona label 6300z)

• Label: 6300.y
• Number of curves: $2$
• Conductor: $6300$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6300.y have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6300.y do not have complex multiplication.

Modular form 6300.2.a.y

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 6300.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6300.y1	6300z1	\([0, 0, 0, -720, 7425]\)	\(28311552/49\)	\(71442000\)	\([2]\)	\(2304\)	\(0.40098\)	\(\Gamma_0(N)\)-optimal
6300.y2	6300z2	\([0, 0, 0, -495, 12150]\)	\(-574992/2401\)	\(-56010528000\)	\([2]\)	\(4608\)	\(0.74755\)