Elliptic curve isogeny class with Cremona label 31200bp (LMFDB label 31200.c)

• Label: 31200bp
• Number of curves: $2$
• Conductor: $31200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 31200bp 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 31200.2.a.bp

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 31200bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31200.c1	31200bp1	\([0, -1, 0, -72558, -7496388]\)	\(42246001231552/14414517\)	\(14414517000000\)	\([2]\)	\(98304\)	\(1.4965\)	\(\Gamma_0(N)\)-optimal
31200.c2	31200bp2	\([0, -1, 0, -62433, -9673263]\)	\(-420526439488/390971529\)	\(-25022177856000000\)	\([2]\)	\(196608\)	\(1.8431\)