Elliptic curve isogeny class with LMFDB label 30600.cf (Cremona label 30600ci)

• Label: 30600.cf
• Number of curves: $2$
• Conductor: $30600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 30600.cf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30600.cf do not have complex multiplication.

Modular form 30600.2.a.cf

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 30600.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30600.cf1	30600ci1	\([0, 0, 0, -975, -4750]\)	\(35152/17\)	\(49572000000\)	\([2]\)	\(24576\)	\(0.74582\)	\(\Gamma_0(N)\)-optimal
30600.cf2	30600ci2	\([0, 0, 0, 3525, -36250]\)	\(415292/289\)	\(-3370896000000\)	\([2]\)	\(49152\)	\(1.0924\)