Elliptic curve isogeny class with Cremona label 6300i (LMFDB label 6300.e)

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

Rank

The elliptic curves in class 6300i 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
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 6300.2.a.i

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 6300i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6300.e2	6300i1	\([0, 0, 0, 15, 65]\)	\(1280/7\)	\(-2041200\)	\([]\)	\(864\)	\(-0.10718\)	\(\Gamma_0(N)\)-optimal
6300.e1	6300i2	\([0, 0, 0, -885, 10145]\)	\(-262885120/343\)	\(-100018800\)	\([]\)	\(2592\)	\(0.44213\)