Elliptic curve isogeny class with LMFDB label 30960.bd (Cremona label 30960q)

• Label: 30960.bd
• Number of curves: $4$
• Conductor: $30960$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 30960.bd have rank \(0\).

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.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 30960.bd do not have complex multiplication.

Modular form 30960.2.a.bd

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 30960.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30960.bd1	30960q4	\([0, 0, 0, -2338347, 1376268986]\)	\(947094050118111698/20769216075\)	\(31008273446246400\)	\([4]\)	\(655360\)	\(2.2801\)
30960.bd2	30960q2	\([0, 0, 0, -151347, 19891586]\)	\(513591322675396/68238500625\)	\(50939767762560000\)	\([2, 2]\)	\(327680\)	\(1.9336\)
30960.bd3	30960q1	\([0, 0, 0, -38847, -2630914]\)	\(34739908901584/4081640625\)	\(761732100000000\)	\([2]\)	\(163840\)	\(1.5870\)	\(\Gamma_0(N)\)-optimal
30960.bd4	30960q3	\([0, 0, 0, 235653, 104954186]\)	\(969360123836302/3748293231075\)	\(-5596171807649126400\)	\([2]\)	\(655360\)	\(2.2801\)