Elliptic curve isogeny class with Cremona label 158400cc (LMFDB label 158400.bc)

• Label: 158400cc
• Number of curves: $4$
• Conductor: $158400$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 158400cc have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400cc do not have complex multiplication.

Modular form 158400.2.a.cc

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 158400cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.bc4	158400cc1	\([0, 0, 0, -40800, 3107000]\)	\(643956736/15125\)	\(176418000000000\)	\([2]\)	\(663552\)	\(1.5192\)	\(\Gamma_0(N)\)-optimal
158400.bc3	158400cc2	\([0, 0, 0, -90300, -5902000]\)	\(436334416/171875\)	\(32076000000000000\)	\([2]\)	\(1327104\)	\(1.8657\)
158400.bc2	158400cc3	\([0, 0, 0, -400800, -96433000]\)	\(610462990336/8857805\)	\(103317437520000000\)	\([2]\)	\(1990656\)	\(2.0685\)
158400.bc1	158400cc4	\([0, 0, 0, -6390300, -6217702000]\)	\(154639330142416/33275\)	\(6209913600000000\)	\([2]\)	\(3981312\)	\(2.4151\)