Elliptic curve isogeny class with Cremona label 30576dc (LMFDB label 30576.cg)

• Label: 30576dc
• Number of curves: $4$
• Conductor: $30576$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 30576dc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30576dc do not have complex multiplication.

Modular form 30576.2.a.dc

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 30576dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30576.cg3	30576dc1	\([0, 1, 0, -5504, -142668]\)	\(38272753/4368\)	\(2104896847872\)	\([2]\)	\(55296\)	\(1.0969\)	\(\Gamma_0(N)\)-optimal
30576.cg2	30576dc2	\([0, 1, 0, -21184, 1030196]\)	\(2181825073/298116\)	\(143659209867264\)	\([2, 2]\)	\(110592\)	\(1.4435\)
30576.cg4	30576dc3	\([0, 1, 0, 33696, 5530356]\)	\(8780064047/32388174\)	\(-15607547014864896\)	\([4]\)	\(221184\)	\(1.7901\)
30576.cg1	30576dc4	\([0, 1, 0, -326944, 71844212]\)	\(8020417344913/187278\)	\(90247452352512\)	\([2]\)	\(221184\)	\(1.7901\)