Elliptic curve isogeny class with Cremona label 30960d (LMFDB label 30960.g)

• Label: 30960d
• Number of curves: $2$
• Conductor: $30960$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 30960d have rank \(2\).

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
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 30960.2.a.d

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 30960d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30960.g1	30960d1	\([0, 0, 0, -2883, -47918]\)	\(3550014724/725625\)	\(541676160000\)	\([2]\)	\(36864\)	\(0.96701\)	\(\Gamma_0(N)\)-optimal
30960.g2	30960d2	\([0, 0, 0, 6117, -287318]\)	\(16954370638/33698025\)	\(-50310881740800\)	\([2]\)	\(73728\)	\(1.3136\)