Elliptic curve isogeny class with Cremona label 100672o (LMFDB label 100672.bi)

• Label: 100672o
• Number of curves: $2$
• Conductor: $100672$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 100672o have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 100672o do not have complex multiplication.

Modular form 100672.2.a.o

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 100672o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100672.bi2	100672o1	\([0, -1, 0, -4033, 49601]\)	\(1890625/832\)	\(3193257852928\)	\([]\)	\(129024\)	\(1.0952\)	\(\Gamma_0(N)\)-optimal
100672.bi1	100672o2	\([0, -1, 0, -158913, -24328511]\)	\(115636266625/8788\)	\(33728786071552\)	\([]\)	\(387072\)	\(1.6445\)