Elliptic curve isogeny class with LMFDB label 30576.v (Cremona label 30576bx)

• Label: 30576.v
• Number of curves: $2$
• Conductor: $30576$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 30576.v have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 30576.2.a.v

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 30576.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30576.v1	30576bx2	\([0, -1, 0, -305188, 64957516]\)	\(104375673106000/69854967\)	\(2103901955221248\)	\([2]\)	\(184320\)	\(1.8788\)
30576.v2	30576bx1	\([0, -1, 0, -15353, 1425684]\)	\(-212629504000/340075827\)	\(-640153295531568\)	\([2]\)	\(92160\)	\(1.5322\)	\(\Gamma_0(N)\)-optimal