Elliptic curve isogeny class with LMFDB label 31200.ca (Cremona label 31200bu)

• Label: 31200.ca
• Number of curves: $4$
• Conductor: $31200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 31200.ca have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 31200.ca do not have complex multiplication.

Modular form 31200.2.a.ca

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 31200.ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31200.ca1	31200bu4	\([0, 1, 0, -17408, -889812]\)	\(72929847752/5265\)	\(42120000000\)	\([2]\)	\(49152\)	\(1.0901\)
31200.ca2	31200bu3	\([0, 1, 0, -6033, 168063]\)	\(379503424/24375\)	\(1560000000000\)	\([2]\)	\(49152\)	\(1.0901\)
31200.ca3	31200bu1	\([0, 1, 0, -1158, -12312]\)	\(171879616/38025\)	\(38025000000\)	\([2, 2]\)	\(24576\)	\(0.74348\)	\(\Gamma_0(N)\)-optimal
31200.ca4	31200bu2	\([0, 1, 0, 2592, -72312]\)	\(240641848/428415\)	\(-3427320000000\)	\([2]\)	\(49152\)	\(1.0901\)