Elliptic curve isogeny class with LMFDB label 30960.c (Cremona label 30960w)

• Label: 30960.c
• Number of curves: $2$
• Conductor: $30960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 30960.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30960.c do not have complex multiplication.

Modular form 30960.2.a.c

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 30960.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30960.c1	30960w2	\([0, 0, 0, -20000043, 34426629658]\)	\(8000051600110940079507/144453125\)	\(15975360000000\)	\([2]\)	\(1146880\)	\(2.5244\)
30960.c2	30960w1	\([0, 0, 0, -1250043, 537879658]\)	\(1953326569433829507/262451171875\)	\(29025000000000000\)	\([2]\)	\(573440\)	\(2.1778\)	\(\Gamma_0(N)\)-optimal