Elliptic curve isogeny class with LMFDB label 380880.dr (Cremona label 380880dr)

• Label: 380880.dr
• Number of curves: $4$
• Conductor: $380880$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 380880.dr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(23\)	\(1\)

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
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 380880.dr do not have complex multiplication.

Modular form 380880.2.a.dr

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 380880.dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
380880.dr1	380880dr3	\([0, 0, 0, -57919152, 169660748279]\)	\(12444451776495616/912525\)	\(1575648348247832400\)	\([2]\)	\(25546752\)	\(2.9425\)
380880.dr2	380880dr4	\([0, 0, 0, -57800127, 170392775834]\)	\(-772993034343376/6661615005\)	\(-184040769150061217383680\)	\([2]\)	\(51093504\)	\(3.2891\)
380880.dr3	380880dr1	\([0, 0, 0, -787152, 182955179]\)	\(31238127616/9703125\)	\(16754294818325250000\)	\([2]\)	\(8515584\)	\(2.3932\)	\(\Gamma_0(N)\)-optimal
380880.dr4	380880dr2	\([0, 0, 0, 2188473, 1236921554]\)	\(41957807024/48205125\)	\(-1331765386519037472000\)	\([2]\)	\(17031168\)	\(2.7398\)