Elliptic curve isogeny class with Cremona label 338130dp (LMFDB label 338130.dp)

• Label: 338130dp
• Number of curves: $4$
• Conductor: $338130$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 338130dp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 338130dp do not have complex multiplication.

Modular form 338130.2.a.dp

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 338130dp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338130.dp4	338130dp1	\([1, -1, 1, 10397443, -488782011]\)	\(7064514799444439/4094064000000\)	\(-72040328419713264000000\)	\([2]\)	\(29859840\)	\(3.0754\)	\(\Gamma_0(N)\)-optimal
338130.dp3	338130dp2	\([1, -1, 1, -41622557, -3880486011]\)	\(453198971846635561/261896250564000\)	\(4608401798926952569764000\)	\([2]\)	\(59719680\)	\(3.4220\)
338130.dp2	338130dp3	\([1, -1, 1, -138834932, 679234839639]\)	\(-16818951115904497561/1592332281446400\)	\(-28019137099153786955366400\)	\([2]\)	\(89579520\)	\(3.6247\)
338130.dp1	338130dp4	\([1, -1, 1, -2269574132, 41616700941399]\)	\(73474353581350183614361/576510977802240\)	\(10144453085844137502474240\)	\([2]\)	\(179159040\)	\(3.9713\)