Elliptic curve isogeny class with Cremona label 304704cc (LMFDB label 304704.cc)

• Label: 304704cc
• Number of curves: $4$
• Conductor: $304704$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 304704cc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 304704cc do not have complex multiplication.

Modular form 304704.2.a.cc

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 304704cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
304704.cc3	304704cc1	\([0, 0, 0, -3948456, -3019849400]\)	\(61604313088/621\)	\(68625591575860224\)	\([2]\)	\(6488064\)	\(2.3895\)	\(\Gamma_0(N)\)-optimal
304704.cc2	304704cc2	\([0, 0, 0, -4043676, -2866545200]\)	\(4135597648/385641\)	\(681863877897747185664\)	\([2, 2]\)	\(12976128\)	\(2.7361\)
304704.cc1	304704cc3	\([0, 0, 0, -14327436, 17663953264]\)	\(45989074372/7555707\)	\(53437924653023446106112\)	\([2]\)	\(25952256\)	\(3.0827\)
304704.cc4	304704cc4	\([0, 0, 0, 4716564, -13585574864]\)	\(1640689628/12223143\)	\(-86448481215210034495488\)	\([2]\)	\(25952256\)	\(3.0827\)